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+{"segments": [{"id": 1, "seek": 3536, "start": 20.91, "end": 35.37, "text": "بسم الله الرحمن الرحيم في المحاضرة اليوم هناخد انتباه المقدمة البسيطة عن ال infinite series اللي بدأناها في المحاضرة السابقة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8978, 9673, 5016, 46958, 25720, 45595, 20498, 8032, 1863, 47283, 3215, 16472, 2655, 3555, 40294, 9673, 28543, 46007, 29739, 3794, 1829, 9566, 3660, 18871, 2423, 13785, 2638, 13672, 1829, 47525, 10721, 8315, 11296, 8978, 9673, 5016, 46958, 25720, 21136, 16758, 28671], "avg_logprob": -0.07326133257033778, "compression_ratio": 1.6044776119402986, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 20.91, "end": 21.23, "word": "بسم", "probability": 0.931640625}, {"start": 21.23, "end": 21.43, "word": " الله", "probability": 0.95849609375}, {"start": 21.43, "end": 21.85, "word": " الرحمن", "probability": 0.9710286458333334}, {"start": 21.85, "end": 22.45, "word": " الرحيم", "probability": 0.9951171875}, 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partial sums exist و بالساوية sum real number S الآن باخد ال limit للطرفين في ال star هنا", "tokens": [10721, 8315, 6156, 9640, 11242, 14739, 2423, 2638, 41881, 11933, 15730, 2423, 4948, 24976, 8310, 295, 14641, 34499, 2514, 4032, 20666, 3794, 995, 2407, 10632, 2408, 957, 1230, 318, 6024, 48506, 4724, 47283, 3215, 2423, 4948, 24976, 9566, 28480, 9957, 8978, 2423, 3543, 34105], "avg_logprob": -0.33385415607028535, "compression_ratio": 1.3178807947019868, "no_speech_prob": 0.0, "words": [{"start": 139.15, "end": 139.91, "word": "أنا", "probability": 0.6248779296875}, {"start": 139.91, "end": 140.67, "word": " فارض", "probability": 0.8030598958333334}, {"start": 140.67, "end": 140.83, "word": " أن", "probability": 0.4580078125}, {"start": 140.83, "end": 140.99, "word": " ال", "probability": 0.7861328125}, {"start": 140.99, "end": 141.31, "word": " series", "probability": 0.441162109375}, {"start": 141.31, "end": 142.15, "word": " converge", "probability": 0.7802734375}, {"start": 142.15, 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190.04, "end": 190.42, "word": "the", "probability": 0.45361328125}, {"start": 190.42, "end": 191.26, "word": " converse", "probability": 0.703369140625}, {"start": 191.26, "end": 195.9, "word": " of", "probability": 0.94970703125}, {"start": 195.9, "end": 196.5, "word": " above", "probability": 0.931640625}, {"start": 196.5, "end": 197.08, "word": " theorem", "probability": 0.87841796875}, {"start": 197.08, "end": 203.14, "word": " is", "probability": 0.9541015625}, {"start": 203.14, "end": 203.84, "word": " false", "probability": 0.900390625}, {"start": 203.84, "end": 207.86, "word": " عكس", "probability": 0.96630859375}, {"start": 207.86, "end": 208.4, "word": " النظرية", "probability": 0.8450927734375}, {"start": 208.4, "end": 209.02, "word": " السابقة", "probability": 0.98681640625}, {"start": 209.02, "end": 209.62, "word": " ليس", "probability": 0.913330078125}, {"start": 209.62, "end": 211.0, "word": " صحيحا", "probability": 0.960546875}, {"start": 211.0, "end": 213.62, "word": " بمعنى", "probability": 0.966796875}, {"start": 213.62, "end": 214.76, "word": " لو", "probability": 0.95947265625}, {"start": 214.76, "end": 215.4, "word": " كانت", "probability": 0.98779296875}, {"start": 215.4, "end": 215.76, "word": " x", "probability": 0.68212890625}, {"start": 215.76, "end": 216.12, "word": " in", "probability": 0.302978515625}], "temperature": 1.0}, {"id": 10, "seek": 23831, "start": 218.35, "end": 238.31, "text": "converge to zero هذا لا يؤدي بالضرورة .. لا يؤدي مش شرط يؤدي ان ال series sigma x in converge وهي مثال على ذلك ناخد مثال", "tokens": [1671, 331, 432, 281, 4018, 23758, 20193, 7251, 33604, 16254, 20666, 11242, 2288, 13063, 3660, 4386, 20193, 7251, 33604, 16254, 37893, 13412, 2288, 9566, 7251, 33604, 16254, 16472, 2423, 2638, 12771, 2031, 294, 41881, 37037, 1829, 50113, 6027, 15844, 29910, 23275, 8717, 47283, 3215, 50113, 6027], "avg_logprob": -0.251662237847105, "compression_ratio": 1.372093023255814, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 218.35, "end": 219.25, "word": "converge", "probability": 0.8092447916666666}, {"start": 219.25, "end": 219.85, "word": " to", "probability": 0.8798828125}, {"start": 219.85, "end": 220.31, "word": " zero", "probability": 0.64306640625}, {"start": 220.31, "end": 222.65, "word": " هذا", "probability": 0.51513671875}, {"start": 222.65, "end": 222.95, "word": " لا", "probability": 0.71337890625}, {"start": 222.95, "end": 223.53, "word": " يؤدي", "probability": 0.8787434895833334}, {"start": 223.53, "end": 224.43, "word": " بالضرورة", "probability": 0.97109375}, {"start": 224.43, "end": 224.61, "word": " ..", "probability": 0.2496337890625}, {"start": 224.61, "end": 224.81, "word": " لا", "probability": 0.260498046875}, {"start": 224.81, "end": 225.49, "word": " يؤدي", "probability": 0.9674479166666666}, {"start": 225.49, "end": 228.23, "word": " مش", "probability": 0.69482421875}, {"start": 228.23, "end": 228.59, "word": " شرط", "probability": 0.96435546875}, {"start": 228.59, "end": 228.97, "word": " يؤدي", "probability": 0.9638671875}, {"start": 228.97, "end": 229.17, "word": " ان", "probability": 0.404541015625}, {"start": 229.17, "end": 229.39, "word": " ال", "probability": 0.7353515625}, {"start": 229.39, "end": 229.73, "word": " series", "probability": 0.78271484375}, {"start": 229.73, "end": 230.93, "word": " sigma", "probability": 0.578125}, {"start": 230.93, "end": 231.29, "word": " x", "probability": 0.78173828125}, {"start": 231.29, "end": 231.71, "word": " in", "probability": 0.779296875}, {"start": 231.71, "end": 234.03, "word": " converge", "probability": 0.38671875}, {"start": 234.03, "end": 236.31, "word": " وهي", "probability": 0.7490234375}, {"start": 236.31, "end": 236.79, "word": " مثال", "probability": 0.98046875}, {"start": 236.79, "end": 236.97, "word": " على", "probability": 0.822265625}, {"start": 236.97, "end": 237.41, "word": " ذلك", "probability": 0.991943359375}, {"start": 237.41, "end": 237.83, "word": " ناخد", "probability": 0.8128255208333334}, {"start": 237.83, "end": 238.31, "word": " مثال", "probability": 0.80712890625}], "temperature": 1.0}, {"id": 11, "seek": 26552, "start": 257.84, "end": 265.52, "text": "example the harmonic series satisfies", "tokens": [3121, 335, 781, 264, 32270, 2638, 44271], "avg_logprob": -0.4367675743997097, "compression_ratio": 0.8604651162790697, "no_speech_prob": 0.0, "words": [{"start": 257.84000000000003, "end": 259.24, "word": "example", "probability": 0.6685994466145834}, {"start": 259.24, "end": 260.64, "word": " the", "probability": 0.58349609375}, {"start": 260.64, "end": 261.24, "word": " harmonic", "probability": 0.83935546875}, {"start": 261.24, "end": 262.04, "word": " series", "probability": 0.89599609375}, {"start": 262.04, "end": 265.52, "word": " satisfies", "probability": 0.7978515625}], "temperature": 1.0}, {"id": 12, "seek": 30456, "start": 279.92, "end": 304.56, "text": "إن ال limit ل xn عبارة عن ال limit ل 1 على n يسوى سفر لكن however .. however ال series ال harmonic series diverges", "tokens": [28814, 1863, 2423, 4948, 5296, 2031, 77, 6225, 3555, 9640, 3660, 18871, 2423, 4948, 5296, 502, 15844, 297, 7251, 3794, 2407, 7578, 8608, 5172, 2288, 44381, 4461, 4386, 4461, 2423, 2638, 2423, 32270, 2638, 18558, 2880], "avg_logprob": -0.3122888416857333, "compression_ratio": 1.3153153153153154, "no_speech_prob": 0.0, "words": [{"start": 279.92, "end": 280.28, "word": "إن", "probability": 0.7127685546875}, {"start": 280.28, "end": 280.46, "word": " ال", "probability": 0.6943359375}, {"start": 280.46, "end": 280.84, "word": " limit", "probability": 0.88330078125}, {"start": 280.84, "end": 282.02, "word": " ل", "probability": 0.91162109375}, {"start": 282.02, "end": 282.98, "word": " xn", "probability": 0.398681640625}, {"start": 282.98, "end": 284.54, "word": " عبارة", "probability": 0.82342529296875}, {"start": 284.54, "end": 284.74, "word": " عن", "probability": 0.99853515625}, {"start": 284.74, "end": 284.88, "word": " ال", "probability": 0.62890625}, {"start": 284.88, "end": 285.28, "word": " limit", "probability": 0.9755859375}, {"start": 285.28, "end": 285.7, "word": " ل", "probability": 0.88916015625}, {"start": 285.7, "end": 286.04, "word": " 1", "probability": 0.53369140625}, {"start": 286.04, "end": 286.42, "word": " على", "probability": 0.619140625}, {"start": 286.42, "end": 286.88, "word": " n", "probability": 0.8193359375}, {"start": 286.88, "end": 288.08, "word": " يسوى", "probability": 0.65740966796875}, {"start": 288.08, "end": 288.6, "word": " سفر", "probability": 0.8740234375}, {"start": 288.6, "end": 291.56, "word": " لكن", "probability": 0.845703125}, {"start": 291.56, "end": 294.1, "word": " however", "probability": 0.88671875}, {"start": 294.1, "end": 294.6, "word": " ..", "probability": 0.2705078125}, {"start": 294.6, "end": 299.42, "word": " however", "probability": 0.900390625}, {"start": 299.42, "end": 300.96, "word": " ال", "probability": 0.7314453125}, {"start": 300.96, "end": 301.4, "word": " series", "probability": 0.95458984375}, {"start": 301.4, "end": 301.62, "word": " ال", "probability": 0.51611328125}, {"start": 301.62, "end": 302.02, "word": " harmonic", "probability": 0.90869140625}, {"start": 302.02, "end": 302.72, "word": " series", "probability": 0.9130859375}, {"start": 302.72, "end": 304.56, "word": " diverges", "probability": 0.715576171875}], "temperature": 1.0}, {"id": 13, "seek": 33141, "start": 309.69, "end": 331.41, "text": "ال harmonic series is divergent مش convergent ليش؟ why؟ احنا برهننا الكلام هذا في chapter تلاتة بس كش في section تلاتة خمسة", "tokens": [6027, 32270, 2638, 307, 18558, 6930, 37893, 9652, 6930, 32239, 8592, 22807, 983, 22807, 1975, 5016, 8315, 4724, 2288, 3224, 1863, 8315, 2423, 28820, 10943, 23758, 8978, 7187, 6055, 1211, 9307, 3660, 4724, 3794, 9122, 8592, 8978, 3541, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660], "avg_logprob": -0.18284574848540286, "compression_ratio": 1.2627737226277371, "no_speech_prob": 0.0, "words": [{"start": 309.69, "end": 309.99, "word": "ال", "probability": 0.87451171875}, {"start": 309.99, "end": 310.33, "word": " harmonic", "probability": 0.7119140625}, {"start": 310.33, "end": 310.79, "word": " series", "probability": 0.8759765625}, {"start": 310.79, "end": 311.01, "word": " is", "probability": 0.9140625}, {"start": 311.01, "end": 311.51, "word": " divergent", "probability": 0.777587890625}, {"start": 311.51, "end": 311.71, "word": " مش", "probability": 0.8349609375}, {"start": 311.71, "end": 312.43, "word": " convergent", "probability": 0.885009765625}, {"start": 312.43, "end": 314.99, "word": " ليش؟", "probability": 0.7750651041666666}, {"start": 314.99, "end": 322.77, "word": " why؟", "probability": 0.885009765625}, {"start": 322.77, "end": 323.13, "word": " احنا", "probability": 0.9308268229166666}, {"start": 323.13, "end": 323.77, "word": " برهننا", "probability": 0.89462890625}, {"start": 323.77, "end": 324.15, "word": " الكلام", "probability": 0.9541015625}, {"start": 324.15, "end": 324.61, "word": " هذا", "probability": 0.8662109375}, {"start": 324.61, "end": 325.85, "word": " في", "probability": 0.97802734375}, {"start": 325.85, "end": 327.15, "word": " chapter", "probability": 0.92724609375}, {"start": 327.15, "end": 327.99, "word": " تلاتة", "probability": 0.91748046875}, {"start": 327.99, "end": 328.77, "word": " بس", "probability": 0.57391357421875}, {"start": 328.77, "end": 329.15, "word": " كش", "probability": 0.53564453125}, {"start": 329.15, "end": 329.33, "word": " في", "probability": 0.8466796875}, {"start": 329.33, "end": 330.31, "word": " section", "probability": 0.446533203125}, {"start": 330.31, "end": 330.85, "word": " تلاتة", "probability": 0.960693359375}, {"start": 330.85, "end": 331.41, "word": " خمسة", "probability": 0.9788818359375}], "temperature": 1.0}, {"id": 14, "seek": 36374, "start": 336.62, "end": 363.74, "text": "فاكرين ان ال sequence هذه كانت طيب نجاوب ليه ال harmonic series diverges في عندي جوابين answer one الإجابة الأولى في عندي مثال أخدنا", "tokens": [5172, 995, 37983, 9957, 16472, 2423, 8310, 29538, 25961, 2655, 23032, 1829, 3555, 8717, 7435, 995, 37746, 32239, 3224, 2423, 32270, 2638, 18558, 2880, 8978, 18871, 16254, 10874, 14407, 3555, 9957, 1867, 472, 33688, 7435, 16758, 3660, 16247, 12610, 7578, 8978, 18871, 16254, 50113, 6027, 5551, 9778, 3215, 8315], "avg_logprob": -0.18609374523162842, "compression_ratio": 1.364864864864865, "no_speech_prob": 0.0, "words": [{"start": 336.62, "end": 337.3, "word": "فاكرين", "probability": 0.9510498046875}, {"start": 337.3, "end": 337.52, "word": " ان", "probability": 0.471435546875}, {"start": 337.52, "end": 337.98, "word": " ال", "probability": 0.53857421875}, {"start": 337.98, "end": 338.44, "word": " sequence", "probability": 0.734375}, {"start": 338.44, "end": 339.04, "word": " هذه", "probability": 0.62109375}, {"start": 339.04, "end": 339.82, "word": " كانت", "probability": 0.93017578125}, {"start": 339.82, "end": 342.02, "word": " طيب", "probability": 0.7650553385416666}, {"start": 342.02, "end": 344.32, "word": " نجاوب", "probability": 0.78631591796875}, {"start": 344.32, "end": 344.76, "word": " ليه", "probability": 0.9697265625}, {"start": 344.76, "end": 344.98, "word": " ال", "probability": 0.91162109375}, {"start": 344.98, "end": 345.4, "word": " harmonic", "probability": 0.93701171875}, {"start": 345.4, "end": 345.9, "word": " series", "probability": 0.85107421875}, {"start": 345.9, "end": 346.76, "word": " diverges", "probability": 0.741943359375}, {"start": 346.76, "end": 347.54, "word": " في", "probability": 0.386474609375}, {"start": 347.54, "end": 347.8, "word": " عندي", "probability": 0.876708984375}, {"start": 347.8, "end": 348.42, "word": " جوابين", "probability": 0.948974609375}, {"start": 348.42, "end": 349.78, "word": " answer", "probability": 0.94873046875}, {"start": 349.78, "end": 352.72, "word": " one", "probability": 0.76953125}, {"start": 352.72, "end": 354.1, "word": " الإجابة", "probability": 0.9136962890625}, {"start": 354.1, "end": 356.64, "word": " الأولى", "probability": 0.9886067708333334}, {"start": 356.64, "end": 360.66, "word": " في", "probability": 0.87841796875}, {"start": 360.66, "end": 361.04, "word": " عندي", "probability": 0.989501953125}, {"start": 361.04, "end": 361.72, "word": " مثال", "probability": 0.968994140625}, {"start": 361.72, "end": 363.74, "word": " أخدنا", "probability": 0.9461669921875}], "temperature": 1.0}, {"id": 15, "seek": 39483, "start": 368.53, "end": 394.83, "text": "by example لسه ماخدينه اللي كان هذا الجزء اللي بتعلق فيه اللي هو ال sequence of partial sums لل series هذه اثبتنا انها not cauchy صح؟ وكان هذا جزء من ايه؟ من تكملة البرهان صح؟ اذا نشوف الرقم تبعها بالظبط section", "tokens": [2322, 1365, 5296, 3794, 3224, 3714, 47283, 3215, 9957, 3224, 13672, 1829, 25961, 23758, 25724, 11622, 38207, 13672, 1829, 39894, 30241, 4587, 8978, 3224, 13672, 1829, 31439, 2423, 8310, 295, 14641, 34499, 24976, 2638, 29538, 1975, 12984, 3555, 2655, 8315, 16472, 11296, 406, 1335, 625, 88, 20328, 5016, 22807, 4032, 41361, 23758, 10874, 11622, 38207, 9154, 1975, 1829, 3224, 22807, 9154, 6055, 24793, 37977, 2423, 26890, 3224, 7649, 20328, 5016, 22807, 1975, 15730, 8717, 8592, 38688, 34892, 4587, 2304, 6055, 3555, 3615, 11296, 20666, 19913, 3555, 9566, 3541], "avg_logprob": -0.1501931193169583, "compression_ratio": 1.5942028985507246, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 368.53, "end": 369.05, "word": "by", "probability": 0.638671875}, {"start": 369.05, "end": 370.01, "word": " example", "probability": 0.958984375}, {"start": 370.01, "end": 372.67, "word": " لسه", "probability": 0.9337565104166666}, {"start": 372.67, "end": 373.33, "word": " ماخدينه", "probability": 0.8720703125}, {"start": 373.33, "end": 373.57, "word": " اللي", "probability": 0.76513671875}, {"start": 373.57, "end": 373.81, "word": " كان", "probability": 0.9814453125}, {"start": 373.81, "end": 374.03, "word": " هذا", "probability": 0.88623046875}, {"start": 374.03, "end": 374.31, "word": " الجزء", "probability": 0.9505208333333334}, {"start": 374.31, "end": 374.43, "word": " اللي", "probability": 0.8994140625}, {"start": 374.43, "end": 374.93, "word": " بتعلق", "probability": 0.8746744791666666}, {"start": 374.93, "end": 375.73, "word": " فيه", "probability": 0.97021484375}, {"start": 375.73, "end": 376.49, "word": " اللي", "probability": 0.970947265625}, {"start": 376.49, "end": 376.71, "word": " هو", "probability": 0.9833984375}, {"start": 376.71, "end": 376.85, "word": " ال", "probability": 0.5439453125}, {"start": 376.85, "end": 377.13, "word": " sequence", "probability": 0.93505859375}, {"start": 377.13, "end": 377.51, "word": " of", "probability": 0.95556640625}, {"start": 377.51, "end": 377.93, "word": " partial", "probability": 0.9462890625}, {"start": 377.93, "end": 378.37, "word": " sums", "probability": 0.9677734375}, {"start": 378.37, "end": 378.59, "word": " لل", "probability": 0.60888671875}, {"start": 378.59, "end": 379.01, "word": " series", "probability": 0.8486328125}, {"start": 379.01, "end": 379.47, "word": " هذه", "probability": 0.76953125}, {"start": 379.47, "end": 381.71, "word": " اثبتنا", "probability": 0.8841796875}, {"start": 381.71, "end": 382.15, "word": " انها", "probability": 0.856201171875}, {"start": 382.15, "end": 382.61, "word": " not", "probability": 0.9453125}, {"start": 382.61, "end": 383.11, "word": " cauchy", "probability": 0.649658203125}, {"start": 383.11, "end": 384.53, "word": " صح؟", "probability": 0.80322265625}, {"start": 384.53, "end": 384.89, "word": " وكان", "probability": 0.8076171875}, {"start": 384.89, "end": 385.13, "word": " هذا", "probability": 0.9609375}, {"start": 385.13, "end": 385.47, "word": " جزء", "probability": 0.9964192708333334}, {"start": 385.47, "end": 385.69, "word": " من", "probability": 0.9931640625}, {"start": 385.69, "end": 386.35, "word": " ايه؟", "probability": 0.79248046875}, {"start": 386.35, "end": 386.57, "word": " من", "probability": 0.98779296875}, {"start": 386.57, "end": 387.05, "word": " تكملة", "probability": 0.93896484375}, {"start": 387.05, "end": 387.61, "word": " البرهان", "probability": 0.77996826171875}, {"start": 387.61, "end": 389.17, "word": " صح؟", "probability": 0.94140625}, {"start": 389.17, "end": 389.47, "word": " اذا", "probability": 0.873046875}, {"start": 389.47, "end": 390.67, "word": " نشوف", "probability": 0.9264322916666666}, {"start": 390.67, "end": 391.17, "word": " الرقم", "probability": 0.970703125}, {"start": 391.17, "end": 391.61, "word": " تبعها", "probability": 0.949462890625}, {"start": 391.61, "end": 392.21, "word": " بالظبط", "probability": 0.9927978515625}, {"start": 392.21, "end": 394.83, "word": " section", "probability": 0.580078125}], "temperature": 1.0}, {"id": 16, "seek": 42337, "start": 397.49, "end": 423.37, "text": "مثال تلاتة خمسة ستة الجزء C by this example the sequence of partial sums Sn where", "tokens": [2304, 12984, 6027, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660, 8608, 2655, 3660, 25724, 11622, 38207, 383, 538, 341, 1365, 264, 8310, 295, 14641, 34499, 9264, 689], "avg_logprob": -0.16702585795830036, "compression_ratio": 1.02, "no_speech_prob": 0.0, "words": [{"start": 397.49, "end": 398.27, "word": "مثال", "probability": 0.9694010416666666}, {"start": 398.27, "end": 400.21, "word": " تلاتة", "probability": 0.927978515625}, {"start": 400.21, "end": 402.99, "word": " خمسة", "probability": 0.923583984375}, {"start": 402.99, "end": 404.73, "word": " ستة", "probability": 0.9137369791666666}, {"start": 404.73, "end": 405.89, "word": " الجزء", "probability": 0.9412434895833334}, {"start": 405.89, "end": 406.29, "word": " C", "probability": 0.67626953125}, {"start": 406.29, "end": 406.75, "word": " by", "probability": 0.60888671875}, {"start": 406.75, "end": 407.07, "word": " this", "probability": 0.9658203125}, {"start": 407.07, "end": 407.75, "word": " example", "probability": 0.9755859375}, {"start": 407.75, "end": 410.87, "word": " the", "probability": 0.6875}, {"start": 410.87, "end": 411.41, "word": " sequence", "probability": 0.974609375}, {"start": 411.41, "end": 412.01, "word": " of", "probability": 0.9658203125}, {"start": 412.01, "end": 412.73, "word": " partial", "probability": 0.93603515625}, {"start": 412.73, "end": 413.49, "word": " sums", "probability": 0.96875}, {"start": 413.49, "end": 422.43, "word": " Sn", "probability": 0.1976318359375}, {"start": 422.43, "end": 423.37, "word": " where", "probability": 0.78955078125}], "temperature": 1.0}, {"id": 17, "seek": 45485, "start": 425.75, "end": 454.85, "text": "SN بيساوي سيجما من K بيساوي واحد إلى N لواحد على K اللي هو واحد زاد نص زاد واحد على N أثبتنا إن ال sequence هذه is not Cauchy is not Cauchy and therefore not convergent", "tokens": [32481, 4724, 1829, 3794, 995, 45865, 8608, 1829, 7435, 15042, 9154, 591, 4724, 1829, 3794, 995, 45865, 36764, 24401, 30731, 426, 5296, 14407, 24401, 15844, 591, 13672, 1829, 31439, 36764, 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431.51, "word": " N", "probability": 0.93896484375}, {"start": 431.51, "end": 433.15, "word": " لواحد", "probability": 0.7176920572916666}, {"start": 433.15, "end": 433.39, "word": " على", "probability": 0.82177734375}, {"start": 433.39, "end": 433.89, "word": " K", "probability": 0.9697265625}, {"start": 433.89, "end": 434.99, "word": " اللي", "probability": 0.85986328125}, {"start": 434.99, "end": 435.25, "word": " هو", "probability": 0.98486328125}, {"start": 435.25, "end": 435.75, "word": " واحد", "probability": 0.9677734375}, {"start": 435.75, "end": 436.23, "word": " زاد", "probability": 0.84423828125}, {"start": 436.23, "end": 436.71, "word": " نص", "probability": 0.828369140625}, {"start": 436.71, "end": 437.79, "word": " زاد", "probability": 0.975341796875}, {"start": 437.79, "end": 439.63, "word": " واحد", "probability": 0.946533203125}, {"start": 439.63, "end": 439.85, "word": " على", "probability": 0.87158203125}, {"start": 439.85, "end": 440.19, "word": " N", "probability": 0.974609375}, {"start": 440.19, "end": 440.87, "word": " أثبتنا", "probability": 0.97041015625}, {"start": 440.87, "end": 441.03, "word": " إن", "probability": 0.63916015625}, {"start": 441.03, "end": 441.15, "word": " ال", "probability": 0.83203125}, {"start": 441.15, "end": 441.55, "word": " sequence", "probability": 0.58544921875}, {"start": 441.55, "end": 442.09, "word": " هذه", "probability": 0.73974609375}, {"start": 442.09, "end": 444.27, "word": " is", "probability": 0.83056640625}, {"start": 444.27, "end": 444.71, "word": " not", "probability": 0.96044921875}, {"start": 444.71, "end": 445.33, "word": " Cauchy", "probability": 0.8719075520833334}, {"start": 445.33, "end": 446.25, "word": " is", "probability": 0.54833984375}, {"start": 446.25, "end": 446.73, "word": " not", "probability": 0.95947265625}, {"start": 446.73, "end": 449.25, "word": " Cauchy", "probability": 0.9368489583333334}, {"start": 449.25, "end": 450.63, "word": " and", "probability": 0.87060546875}, {"start": 450.63, "end": 451.29, "word": " therefore", "probability": 0.84716796875}, {"start": 451.29, "end": 454.03, "word": " not", "probability": 0.875}, {"start": 454.03, "end": 454.85, "word": " convergent", "probability": 0.958740234375}], "temperature": 1.0}, {"id": 18, "seek": 47787, "start": 460.33, "end": 477.87, "text": "حسب by cushy by cushy criterion cushy criterion بتقول أي sequence of real numbers is convergent if and only if it is cushy اللي إحنا أثبتنا إن ال sequence هذه في المثال هذا", "tokens": [5016, 35457, 538, 18422, 88, 538, 18422, 88, 46691, 18422, 88, 46691, 39894, 39648, 36632, 8310, 295, 957, 3547, 307, 9652, 6930, 498, 293, 787, 498, 309, 307, 18422, 88, 13672, 1829, 11933, 5016, 8315, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 8310, 29538, 8978, 9673, 12984, 6027, 23758], "avg_logprob": -0.2737499862909317, "compression_ratio": 1.436241610738255, "no_speech_prob": 0.0, "words": [{"start": 460.33, "end": 460.93, "word": "حسب", "probability": 0.77978515625}, {"start": 460.93, "end": 461.69, "word": " by", "probability": 0.7021484375}, {"start": 461.69, "end": 463.01, "word": " cushy", "probability": 0.60650634765625}, {"start": 463.01, "end": 464.97, "word": " by", "probability": 0.1129150390625}, {"start": 464.97, "end": 465.69, "word": " cushy", "probability": 0.92138671875}, {"start": 465.69, "end": 466.47, "word": " criterion", "probability": 0.9482421875}, {"start": 466.47, "end": 469.11, "word": " cushy", "probability": 0.547088623046875}, {"start": 469.11, "end": 469.51, "word": " criterion", "probability": 0.97265625}, {"start": 469.51, "end": 469.85, "word": " بتقول", "probability": 0.8955078125}, {"start": 469.85, "end": 470.05, "word": " أي", "probability": 0.7548828125}, {"start": 470.05, "end": 470.45, "word": " sequence", "probability": 0.88818359375}, {"start": 470.45, "end": 470.65, "word": " of", "probability": 0.955078125}, {"start": 470.65, "end": 470.85, "word": " real", "probability": 0.97265625}, {"start": 470.85, "end": 471.33, "word": " numbers", "probability": 0.83935546875}, {"start": 471.33, "end": 471.55, "word": " is", "probability": 0.9482421875}, {"start": 471.55, "end": 472.31, "word": " convergent", "probability": 0.9677734375}, {"start": 472.31, "end": 472.95, "word": " if", "probability": 0.966796875}, {"start": 472.95, "end": 473.15, "word": " and", "probability": 0.94482421875}, {"start": 473.15, "end": 473.35, "word": " only", "probability": 0.93310546875}, {"start": 473.35, "end": 473.55, "word": " if", "probability": 0.9775390625}, {"start": 473.55, "end": 473.73, "word": " it", "probability": 0.97412109375}, {"start": 473.73, "end": 473.91, "word": " is", "probability": 0.9453125}, {"start": 473.91, "end": 474.75, "word": " cushy", "probability": 0.817138671875}, {"start": 474.75, "end": 475.35, "word": " اللي", "probability": 0.57269287109375}, {"start": 475.35, "end": 475.55, "word": " إحنا", "probability": 0.7461751302083334}, {"start": 475.55, "end": 476.01, "word": " أثبتنا", "probability": 0.93466796875}, {"start": 476.01, "end": 476.11, "word": " إن", "probability": 0.71337890625}, {"start": 476.11, "end": 476.19, "word": " ال", "probability": 0.80712890625}, {"start": 476.19, "end": 476.51, "word": " sequence", "probability": 0.95849609375}, {"start": 476.51, "end": 476.93, "word": " هذه", "probability": 0.546875}, {"start": 476.93, "end": 477.07, "word": " في", "probability": 0.9140625}, {"start": 477.07, "end": 477.53, "word": " المثال", "probability": 0.99072265625}, {"start": 477.53, "end": 477.87, "word": " هذا", "probability": 0.958984375}], "temperature": 1.0}, {"id": 19, "seek": 49102, "start": 479.62, "end": 491.02, "text": "ماهياش كوشي و بالتالي not convergent طب ما هذه هي ال sequence of partial .. هذه هي ال sequence of partial sums لل harmonic series اذا by above definition", "tokens": [15042, 3224, 1829, 33599, 9122, 2407, 8592, 1829, 4032, 20666, 2655, 6027, 1829, 406, 9652, 6930, 23032, 3555, 19446, 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483.08, "end": 483.28, "word": " هي", "probability": 0.91357421875}, {"start": 483.28, "end": 483.4, "word": " ال", "probability": 0.76318359375}, {"start": 483.4, "end": 483.7, "word": " sequence", "probability": 0.9609375}, {"start": 483.7, "end": 484.06, "word": " of", "probability": 0.93505859375}, {"start": 484.06, "end": 484.46, "word": " partial", "probability": 0.9384765625}, {"start": 484.46, "end": 484.56, "word": " ..", "probability": 0.47119140625}, {"start": 484.56, "end": 484.84, "word": " هذه", "probability": 0.86572265625}, {"start": 484.84, "end": 485.02, "word": " هي", "probability": 0.978515625}, {"start": 485.02, "end": 485.12, "word": " ال", "probability": 0.921875}, {"start": 485.12, "end": 485.42, "word": " sequence", "probability": 0.99072265625}, {"start": 485.42, "end": 485.68, "word": " of", "probability": 0.9736328125}, {"start": 485.68, "end": 486.04, "word": " partial", "probability": 0.9560546875}, {"start": 486.04, "end": 486.52, "word": " sums", 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ال", "probability": 0.94287109375}, {"start": 501.13, "end": 501.47, "word": " series", "probability": 0.96923828125}, {"start": 501.47, "end": 501.71, "word": " of", "probability": 0.96484375}, {"start": 501.71, "end": 502.07, "word": " partial", "probability": 0.9560546875}, {"start": 502.07, "end": 502.47, "word": " sums", "probability": 0.89990234375}, {"start": 502.47, "end": 502.79, "word": " is", "probability": 0.94677734375}, {"start": 502.79, "end": 503.05, "word": " not", "probability": 0.97119140625}, {"start": 503.05, "end": 503.83, "word": " convergent", "probability": 0.96923828125}, {"start": 503.83, "end": 504.85, "word": " اذا", "probability": 0.66015625}, {"start": 504.85, "end": 505.05, "word": " ال", "probability": 0.92138671875}, {"start": 505.05, "end": 505.57, "word": " series", "probability": 0.96630859375}, {"start": 505.57, "end": 507.49, "word": " نفسها", "probability": 0.9812825520833334}, {"start": 507.49, "end": 508.31, "word": " is", "probability": 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"word": " two", "probability": 0.46923828125}], "temperature": 1.0}, {"id": 22, "seek": 57248, "start": 545.08, "end": 572.48, "text": "إنه by .. في مثال آخر أثبتنا فيه by example تلاتة تلاتة تلاتة بي .. إذا في section تلاتة تلاتة المثال تلاتة بي أثبتنا فيه إن ال sequence و partial sums", "tokens": [28814, 1863, 3224, 538, 4386, 8978, 50113, 6027, 19753, 34740, 5551, 12984, 3555, 2655, 8315, 8978, 3224, 538, 1365, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 4724, 1829, 4386, 11933, 15730, 8978, 3541, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 9673, 12984, 6027, 6055, 1211, 9307, 3660, 4724, 1829, 5551, 12984, 3555, 2655, 8315, 8978, 3224, 36145, 2423, 8310, 4032, 14641, 34499], "avg_logprob": -0.19202899241792984, "compression_ratio": 1.6985294117647058, "no_speech_prob": 0.0, "words": [{"start": 545.08, "end": 545.78, "word": "إنه", "probability": 0.6820068359375}, {"start": 545.78, "end": 546.68, "word": " by", "probability": 0.74462890625}, {"start": 546.68, "end": 547.78, "word": " ..", "probability": 0.326416015625}, {"start": 547.78, "end": 548.1, "word": " في", "probability": 0.6748046875}, {"start": 548.1, "end": 548.54, "word": " مثال", "probability": 0.994873046875}, {"start": 548.54, "end": 549.1, "word": " آخر", "probability": 0.810546875}, {"start": 549.1, "end": 550.54, "word": " أثبتنا", "probability": 0.98935546875}, {"start": 550.54, "end": 551.38, "word": " فيه", "probability": 0.9892578125}, {"start": 551.38, "end": 552.58, "word": " by", "probability": 0.806640625}, {"start": 552.58, "end": 553.54, "word": " example", "probability": 0.931640625}, {"start": 553.54, "end": 557.9, "word": " تلاتة", "probability": 0.8306884765625}, {"start": 557.9, "end": 558.42, "word": " تلاتة", "probability": 0.8992919921875}, {"start": 558.42, "end": 560.06, "word": " تلاتة", "probability": 0.982666015625}, {"start": 560.06, "end": 561.6, "word": " بي", "probability": 0.68212890625}, {"start": 561.6, "end": 562.64, "word": " ..", "probability": 0.2822265625}, {"start": 562.64, "end": 563.0, "word": " إذا", "probability": 0.44805908203125}, {"start": 563.0, "end": 563.18, "word": " في", "probability": 0.73681640625}, {"start": 563.18, "end": 563.56, "word": " section", "probability": 0.50830078125}, {"start": 563.56, "end": 564.12, "word": " تلاتة", "probability": 0.9847412109375}, {"start": 564.12, "end": 564.8, "word": " تلاتة", "probability": 0.994873046875}, {"start": 564.8, "end": 566.24, "word": " المثال", "probability": 0.9375}, {"start": 566.24, "end": 566.8, "word": " تلاتة", "probability": 0.98974609375}, {"start": 566.8, "end": 567.5, "word": " بي", "probability": 0.984130859375}, {"start": 567.5, "end": 568.8, "word": " أثبتنا", "probability": 0.97255859375}, {"start": 568.8, "end": 569.4, "word": " فيه", "probability": 0.9892578125}, {"start": 569.4, "end": 570.46, "word": " إن", "probability": 0.62548828125}, {"start": 570.46, "end": 570.76, "word": " ال", "probability": 0.75537109375}, {"start": 570.76, "end": 571.18, "word": " sequence", "probability": 0.88232421875}, {"start": 571.18, "end": 571.54, "word": " و", "probability": 0.62548828125}, {"start": 571.54, "end": 571.86, "word": " partial", "probability": 0.955078125}, {"start": 571.86, "end": 572.48, "word": " sums", "probability": 0.95361328125}], "temperature": 1.0}, {"id": 23, "seek": 60242, "start": 574.91, "end": 602.43, "text": "the sequence of partial sums Sn is unbounded أثبتنا بالمثال هذا أن ال sequence Sn of partial sums اللي هي هذه is unbounded and therefore", "tokens": [3322, 8310, 295, 14641, 34499, 9264, 307, 517, 18767, 292, 5551, 12984, 3555, 2655, 8315, 20666, 2304, 12984, 6027, 23758, 14739, 2423, 8310, 9264, 295, 14641, 34499, 13672, 1829, 39896, 29538, 307, 517, 18767, 292, 293, 4412], "avg_logprob": -0.24033717379758232, "compression_ratio": 1.3524590163934427, "no_speech_prob": 0.0, "words": [{"start": 574.91, "end": 575.19, "word": "the", "probability": 0.1629638671875}, {"start": 575.19, "end": 575.83, "word": " sequence", "probability": 0.97607421875}, {"start": 575.83, "end": 576.15, "word": " of", "probability": 0.97412109375}, {"start": 576.15, "end": 576.87, "word": " partial", "probability": 0.9306640625}, {"start": 576.87, "end": 580.91, "word": " sums", "probability": 0.9560546875}, {"start": 580.91, "end": 584.19, "word": " Sn", "probability": 0.22509765625}, {"start": 584.19, "end": 585.67, "word": " is", "probability": 0.90087890625}, {"start": 585.67, "end": 590.37, "word": " unbounded", "probability": 0.9537760416666666}, {"start": 590.37, "end": 591.89, "word": " أثبتنا", "probability": 0.89453125}, {"start": 591.89, "end": 592.41, "word": " بالمثال", "probability": 0.958740234375}, {"start": 592.41, "end": 592.69, "word": " هذا", "probability": 0.890625}, {"start": 592.69, "end": 592.99, "word": " أن", "probability": 0.4599609375}, {"start": 592.99, "end": 593.95, "word": " ال", "probability": 0.50927734375}, {"start": 593.95, "end": 594.39, "word": " sequence", "probability": 0.66357421875}, {"start": 594.39, "end": 595.01, "word": " Sn", "probability": 0.77099609375}, {"start": 595.01, "end": 595.43, "word": " of", "probability": 0.87255859375}, {"start": 595.43, "end": 595.91, "word": " partial", "probability": 0.943359375}, {"start": 595.91, "end": 596.41, "word": " sums", "probability": 0.94775390625}, {"start": 596.41, "end": 597.43, "word": " اللي", "probability": 0.6671142578125}, {"start": 597.43, "end": 597.59, "word": " هي", "probability": 0.6708984375}, {"start": 597.59, "end": 597.97, "word": " هذه", "probability": 0.7890625}, {"start": 597.97, "end": 599.33, "word": " is", "probability": 0.865234375}, {"start": 599.33, "end": 600.21, "word": " unbounded", "probability": 0.9676106770833334}, {"start": 600.21, "end": 601.85, "word": " and", "probability": 0.93603515625}, {"start": 601.85, "end": 602.43, "word": " therefore", "probability": 0.8564453125}], "temperature": 1.0}, {"id": 24, "seek": 62336, "start": 604.44, "end": 623.36, "text": "إذا كانت الـ sequence unbounded إذا بتطلع divergent أو not convergent لأن sn is divergent لأن لو كانت convergent بتكون bounded وبالتالي therefore ال series أو ال harmonic series", "tokens": [28814, 15730, 25961, 2655, 2423, 39184, 8310, 517, 18767, 292, 11933, 15730, 39894, 9566, 1211, 3615, 18558, 6930, 34051, 406, 9652, 6930, 5296, 33456, 2406, 307, 18558, 6930, 5296, 33456, 45164, 25961, 2655, 9652, 6930, 39894, 30544, 37498, 46599, 6027, 2655, 6027, 1829, 4412, 2423, 2638, 34051, 2423, 32270, 2638], "avg_logprob": -0.2749693744322833, "compression_ratio": 1.509933774834437, "no_speech_prob": 0.0, "words": [{"start": 604.44, "end": 604.76, "word": "إذا", "probability": 0.803466796875}, {"start": 604.76, "end": 605.1, "word": " كانت", "probability": 0.98046875}, {"start": 605.1, "end": 605.16, "word": " الـ", "probability": 0.588134765625}, {"start": 605.16, "end": 605.42, "word": " sequence", "probability": 0.8427734375}, {"start": 605.42, "end": 606.34, "word": " unbounded", "probability": 0.8694661458333334}, {"start": 606.34, "end": 606.52, "word": " إذا", "probability": 0.43463134765625}, {"start": 606.52, "end": 606.94, "word": " بتطلع", "probability": 0.9244384765625}, {"start": 606.94, "end": 607.72, "word": " divergent", "probability": 0.6568603515625}, {"start": 607.72, "end": 608.38, "word": " أو", "probability": 0.7763671875}, {"start": 608.38, "end": 608.6, "word": " not", "probability": 0.78076171875}, {"start": 608.6, "end": 609.18, "word": " convergent", "probability": 0.96875}, {"start": 609.18, "end": 609.46, "word": " لأن", "probability": 0.525634765625}, {"start": 609.46, "end": 609.82, "word": " sn", "probability": 0.2176513671875}, {"start": 609.82, "end": 610.52, "word": " is", "probability": 0.7001953125}, {"start": 610.52, "end": 613.18, "word": " divergent", "probability": 0.9091796875}, {"start": 613.18, "end": 615.48, "word": " لأن", "probability": 0.87353515625}, {"start": 615.48, "end": 615.66, "word": " لو", "probability": 0.78955078125}, {"start": 615.66, "end": 616.06, "word": " كانت", "probability": 0.98876953125}, {"start": 616.06, "end": 616.66, "word": " convergent", "probability": 0.908447265625}, {"start": 616.66, "end": 617.08, "word": " بتكون", "probability": 0.92333984375}, {"start": 617.08, "end": 617.58, "word": " bounded", "probability": 0.8720703125}, {"start": 617.58, "end": 619.4, "word": " وبالتالي", "probability": 0.90546875}, {"start": 619.4, "end": 620.04, "word": " therefore", "probability": 0.370361328125}, {"start": 620.04, "end": 620.8, "word": " ال", "probability": 0.88818359375}, {"start": 620.8, "end": 622.02, "word": " series", "probability": 0.7666015625}, {"start": 622.02, "end": 622.46, "word": " أو", "probability": 0.853515625}, {"start": 622.46, "end": 622.58, "word": " ال", "probability": 0.837890625}, {"start": 622.58, "end": 622.84, "word": " harmonic", "probability": 0.67431640625}, {"start": 622.84, "end": 623.36, "word": " series", "probability": 0.93359375}], "temperature": 1.0}, {"id": 25, "seek": 64083, "start": 624.93, "end": 640.83, "text": "divergent إذا هذا برضه إجابة تانية بتخلي ال harmonic series divergent تمام طيب نرجع ناخد أمثلة أخرى", "tokens": [67, 592, 260, 6930, 11933, 15730, 23758, 4724, 43042, 3224, 11933, 7435, 16758, 3660, 6055, 7649, 10632, 39894, 9778, 20292, 2423, 32270, 2638, 18558, 6930, 46811, 10943, 23032, 1829, 3555, 8717, 47341, 3615, 8717, 47283, 3215, 5551, 2304, 12984, 37977, 5551, 34740, 7578], "avg_logprob": -0.26278409971432254, "compression_ratio": 1.2, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 624.93, "end": 626.01, "word": "divergent", "probability": 0.49713134765625}, {"start": 626.01, "end": 626.85, "word": " إذا", "probability": 0.452545166015625}, {"start": 626.85, "end": 627.15, "word": " هذا", "probability": 0.53369140625}, {"start": 627.15, "end": 628.09, "word": " برضه", "probability": 0.8639322916666666}, {"start": 628.09, "end": 628.81, "word": " إجابة", "probability": 0.9791259765625}, {"start": 628.81, "end": 629.35, "word": " تانية", "probability": 0.9920247395833334}, {"start": 629.35, "end": 631.09, "word": " بتخلي", "probability": 0.89208984375}, {"start": 631.09, "end": 631.57, "word": " ال", "probability": 0.348876953125}, {"start": 631.57, "end": 631.93, "word": " harmonic", "probability": 0.64990234375}, {"start": 631.93, "end": 632.47, "word": " series", "probability": 0.86083984375}, {"start": 632.47, "end": 633.35, "word": " divergent", "probability": 0.83203125}, {"start": 633.35, "end": 634.33, "word": " تمام", "probability": 0.736572265625}, {"start": 634.33, "end": 636.97, "word": " طيب", "probability": 0.779541015625}, {"start": 636.97, "end": 637.35, "word": " نرجع", "probability": 0.9187825520833334}, {"start": 637.35, "end": 637.93, "word": " ناخد", "probability": 0.9759114583333334}, {"start": 637.93, "end": 638.93, "word": " أمثلة", "probability": 0.96240234375}, {"start": 638.93, "end": 640.83, "word": " أخرى", "probability": 0.98486328125}], "temperature": 1.0}, {"id": 26, "seek": 69725, "start": 668.59, "end": 697.25, "text": "أول شيء الـ geometric series الـ geometric series اللي هي summation من k بساوي سفر to infinity لR to K اللي الحد الأول تبعها واحد والأساس تبعها R اشمالها واحد", "tokens": [10721, 12610, 44049, 38207, 2423, 39184, 33246, 2638, 2423, 39184, 33246, 2638, 13672, 1829, 39896, 28811, 9154, 350, 4724, 3794, 995, 45865, 8608, 5172, 2288, 281, 13202, 5296, 49, 281, 591, 13672, 1829, 21542, 3215, 16247, 12610, 6055, 3555, 3615, 11296, 36764, 24401, 16070, 10721, 3794, 32277, 6055, 3555, 3615, 11296, 497, 1975, 8592, 2304, 6027, 11296, 36764, 24401], "avg_logprob": -0.2687500034769376, "compression_ratio": 1.5263157894736843, "no_speech_prob": 0.0, "words": [{"start": 668.59, "end": 669.31, "word": "أول", "probability": 0.91943359375}, {"start": 669.31, "end": 669.87, "word": " شيء", "probability": 0.4613037109375}, {"start": 669.87, "end": 670.13, "word": " الـ", "probability": 0.487548828125}, {"start": 670.13, "end": 670.75, "word": " geometric", "probability": 0.64501953125}, {"start": 670.75, "end": 671.61, "word": " series", "probability": 0.89013671875}, {"start": 671.61, "end": 678.59, "word": " الـ", "probability": 0.637451171875}, {"start": 678.59, "end": 678.93, "word": " geometric", "probability": 0.8017578125}, {"start": 678.93, "end": 679.87, "word": " series", "probability": 0.92236328125}, {"start": 679.87, "end": 681.87, "word": " اللي", "probability": 0.57861328125}, {"start": 681.87, "end": 682.23, "word": " هي", "probability": 0.96044921875}, {"start": 682.23, "end": 683.13, "word": " summation", "probability": 0.4921875}, {"start": 683.13, "end": 683.97, "word": " من", "probability": 0.9189453125}, {"start": 683.97, "end": 684.63, "word": " k", "probability": 0.43408203125}, {"start": 684.63, "end": 685.47, "word": " بساوي", "probability": 0.765625}, {"start": 685.47, "end": 686.21, "word": " سفر", "probability": 0.7727864583333334}, {"start": 686.21, "end": 686.97, "word": " to", "probability": 0.5224609375}, {"start": 686.97, "end": 687.61, "word": " infinity", "probability": 0.9072265625}, {"start": 687.61, "end": 688.55, "word": " لR", "probability": 0.5780029296875}, {"start": 688.55, "end": 688.81, "word": " to", "probability": 0.85546875}, {"start": 688.81, "end": 689.29, "word": " K", "probability": 0.61767578125}, {"start": 689.29, "end": 690.37, "word": " اللي", "probability": 0.81005859375}, {"start": 690.37, "end": 690.73, "word": " الحد", "probability": 0.900634765625}, {"start": 690.73, "end": 691.03, "word": " الأول", "probability": 0.945068359375}, {"start": 691.03, "end": 691.51, "word": " تبعها", "probability": 0.8831787109375}, {"start": 691.51, "end": 692.09, "word": " واحد", "probability": 0.926513671875}, {"start": 692.09, "end": 692.75, "word": " والأساس", "probability": 0.881103515625}, {"start": 692.75, "end": 693.37, "word": " ت��عها", "probability": 0.975341796875}, {"start": 693.37, "end": 693.85, "word": " R", "probability": 0.953125}, {"start": 693.85, "end": 696.49, "word": " اشمالها", "probability": 0.75556640625}, {"start": 696.49, "end": 697.25, "word": " واحد", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 27, "seek": 72825, "start": 700.35, "end": 728.25, "text": "converges if absolute r أصغر من one and diverges and its sum its sum بيساوي واحد على واحد minus r", "tokens": [1671, 331, 2880, 498, 8236, 367, 5551, 9381, 17082, 2288, 9154, 472, 293, 18558, 2880, 293, 1080, 2408, 1080, 2408, 4724, 1829, 3794, 995, 45865, 36764, 24401, 15844, 36764, 24401, 3175, 367], "avg_logprob": -0.19779829545454544, "compression_ratio": 1.1214953271028036, "no_speech_prob": 0.0, "words": [{"start": 700.35, "end": 701.75, "word": "converges", "probability": 0.91162109375}, {"start": 701.75, "end": 703.15, "word": " if", "probability": 0.8056640625}, {"start": 703.15, "end": 704.01, "word": " absolute", "probability": 0.79248046875}, {"start": 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1.0}, {"id": 34, "seek": 93900, "start": 910.0, "end": 939.0, "text": "لا يقول لا سفر ال limit تبعته ما بيسويش سفر وبالتالي by the nth term test المسح اه اذا كان limit الحد النوني بيسويش سفر فال test بتقول لي ان ال series is divergent ال series sigma ل R to N من N equal 0 to infinity diverges", "tokens": [15040, 7251, 39648, 20193, 8608, 5172, 2288, 2423, 4948, 6055, 3555, 34268, 3224, 19446, 4724, 1829, 3794, 45865, 8592, 8608, 5172, 2288, 46599, 6027, 2655, 6027, 1829, 538, 264, 297, 392, 1433, 1500, 9673, 3794, 5016, 1975, 3224, 1975, 15730, 25961, 4948, 21542, 3215, 28239, 11536, 1829, 4724, 1829, 3794, 45865, 8592, 8608, 5172, 2288, 6156, 6027, 1500, 39894, 39648, 32239, 16472, 2423, 2638, 307, 18558, 6930, 2423, 2638, 12771, 5296, 497, 281, 426, 9154, 426, 2681, 1958, 281, 13202, 18558, 2880], "avg_logprob": -0.3328313317643591, "compression_ratio": 1.5736040609137056, "no_speech_prob": 0.0, "words": [{"start": 910.0, "end": 910.34, "word": "لا", "probability": 0.384033203125}, {"start": 910.34, "end": 910.72, "word": " يقول", "probability": 0.894775390625}, {"start": 910.72, "end": 910.88, "word": " لا", "probability": 0.141357421875}, {"start": 910.88, "end": 911.28, "word": " سفر", "probability": 0.7975260416666666}, {"start": 911.28, "end": 911.46, "word": " ال", "probability": 0.25244140625}, {"start": 911.46, "end": 911.64, "word": " limit", "probability": 0.80322265625}, {"start": 911.64, "end": 912.16, "word": " تبعته", "probability": 0.70660400390625}, {"start": 912.16, "end": 912.26, "word": " ما", "probability": 0.312255859375}, {"start": 912.26, "end": 912.7, "word": " بيسويش", "probability": 0.803515625}, {"start": 912.7, "end": 913.1, "word": " سفر", "probability": 0.9401041666666666}, {"start": 913.1, "end": 915.46, "word": " وبالتالي", "probability": 0.90537109375}, {"start": 915.46, "end": 915.64, "word": " by", "probability": 0.7265625}, {"start": 915.64, "end": 915.86, "word": " the", "probability": 0.8681640625}, {"start": 915.86, "end": 916.2, "word": " nth", "probability": 0.677001953125}, {"start": 916.2, "end": 916.5, "word": " term", "probability": 0.91943359375}, {"start": 916.5, "end": 916.96, "word": " test", "probability": 0.9501953125}, {"start": 916.96, "end": 918.22, "word": " المسح", "probability": 0.7285970052083334}, {"start": 918.22, "end": 919.66, "word": " اه", "probability": 0.5875244140625}, {"start": 919.66, "end": 920.1, "word": " اذا", "probability": 0.833740234375}, {"start": 920.1, "end": 920.4, "word": " كان", "probability": 0.98876953125}, {"start": 920.4, "end": 920.68, "word": " limit", "probability": 0.91552734375}, {"start": 920.68, "end": 921.06, "word": " الحد", "probability": 0.927978515625}, {"start": 921.06, "end": 921.44, "word": " النوني", "probability": 0.91357421875}, {"start": 921.44, "end": 921.9, "word": " بيسويش", "probability": 0.85322265625}, {"start": 921.9, "end": 922.34, "word": " سفر", "probability": 0.9830729166666666}, {"start": 922.34, "end": 923.98, "word": " فال", "probability": 0.6942138671875}, {"start": 923.98, "end": 924.36, "word": " test", "probability": 0.325927734375}, {"start": 924.36, "end": 925.16, "word": " بتقول", "probability": 0.766357421875}, {"start": 925.16, "end": 925.32, "word": " لي", "probability": 0.29296875}, {"start": 925.32, "end": 925.48, "word": " ان", "probability": 0.578125}, {"start": 925.48, "end": 925.86, "word": " ال", "probability": 0.76953125}, {"start": 925.86, "end": 926.28, "word": " series", "probability": 0.92138671875}, {"start": 926.28, "end": 931.5, "word": " is", "probability": 0.77734375}, {"start": 931.5, "end": 932.32, "word": " divergent", "probability": 0.802490234375}, {"start": 932.32, "end": 932.6, "word": " ال", "probability": 0.7109375}, {"start": 932.6, "end": 932.92, "word": " series", "probability": 0.90283203125}, {"start": 932.92, "end": 933.56, "word": " sigma", "probability": 0.53515625}, {"start": 933.56, "end": 934.42, "word": " ل", "probability": 0.49560546875}, {"start": 934.42, "end": 934.76, "word": " R", "probability": 0.288330078125}, {"start": 934.76, "end": 934.96, "word": " to", "probability": 0.634765625}, {"start": 934.96, "end": 935.28, "word": " N", "probability": 0.90576171875}, {"start": 935.28, "end": 935.5, "word": " من", "probability": 0.85986328125}, {"start": 935.5, "end": 935.76, "word": " N", "probability": 0.86328125}, {"start": 935.76, "end": 936.14, "word": " equal", "probability": 0.38671875}, {"start": 936.14, "end": 936.7, "word": " 0", "probability": 0.37646484375}, {"start": 936.7, "end": 937.48, "word": " to", "probability": 0.66455078125}, {"start": 937.48, "end": 938.02, "word": " infinity", "probability": 0.83984375}, {"start": 938.02, "end": 939.0, "word": " diverges", "probability": 0.8515625}], "temperature": 1.0}, {"id": 35, "seek": 96563, "start": 945.29, "end": 965.63, "text": "لأنه لو كانت convergent فالمفروض limit الحد اللوني يساوي سفر وهذا مش موجود تمام؟ ان انا شوفت هنا كيف أخدنا ال .. او استخدمنا ال in term test لإثبات ال divergence مثال تاني", "tokens": [1211, 33456, 3224, 45164, 25961, 2655, 9652, 6930, 6156, 45340, 5172, 32887, 11242, 4948, 21542, 3215, 13672, 11536, 1829, 7251, 3794, 995, 45865, 8608, 5172, 2288, 37037, 15730, 37893, 3714, 29245, 23328, 46811, 10943, 22807, 16472, 1975, 8315, 13412, 38688, 2655, 34105, 9122, 33911, 5551, 9778, 3215, 8315, 2423, 4386, 1975, 2407, 44713, 9778, 40448, 8315, 2423, 294, 1433, 1500, 5296, 28814, 12984, 3555, 9307, 2423, 47387, 50113, 6027, 6055, 7649, 1829], "avg_logprob": -0.24550513372029345, "compression_ratio": 1.483695652173913, "no_speech_prob": 0.0, "words": [{"start": 945.29, "end": 945.81, "word": "لأنه", "probability": 0.711669921875}, {"start": 945.81, "end": 945.91, "word": " لو", "probability": 0.90771484375}, {"start": 945.91, "end": 946.29, "word": " كانت", "probability": 0.980712890625}, {"start": 946.29, "end": 947.01, "word": " convergent", "probability": 0.655029296875}, {"start": 947.01, "end": 947.65, "word": " فالمفروض", 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{"start": 960.55, "end": 960.71, "word": " ال", "probability": 0.96337890625}, {"start": 960.71, "end": 961.23, "word": " divergence", "probability": 0.99609375}, {"start": 961.23, "end": 965.15, "word": " مثال", "probability": 0.9658203125}, {"start": 965.15, "end": 965.63, "word": " تاني", "probability": 0.9466145833333334}], "temperature": 1.0}, {"id": 36, "seek": 100000, "start": 974.4, "end": 1000.0, "text": "show that ال series اللي متولدة من ال sequence سالب واحد to end اللي هي أول حد هيكون واحد بعدين سالب واحد بعدين واحد بعدين سالب واحد و هكذا", "tokens": [34436, 300, 2423, 2638, 13672, 1829, 44650, 12610, 41891, 9154, 2423, 8310, 8608, 6027, 3555, 36764, 24401, 281, 917, 13672, 1829, 39896, 5551, 12610, 11331, 3215, 39896, 30544, 36764, 24401, 39182, 9957, 8608, 6027, 3555, 36764, 24401, 39182, 9957, 36764, 24401, 39182, 9957, 8608, 6027, 3555, 36764, 24401, 4032, 8032, 4117, 15730], "avg_logprob": -0.12942216643747292, "compression_ratio": 1.7421875, "no_speech_prob": 0.0, "words": [{"start": 974.4000000000001, "end": 975.44, "word": "show", "probability": 0.59375}, {"start": 975.44, "end": 976.48, "word": " that", "probability": 0.8955078125}, {"start": 976.48, "end": 978.44, "word": " ال", "probability": 0.6982421875}, {"start": 978.44, "end": 979.06, "word": " series", "probability": 0.66455078125}, {"start": 979.06, "end": 981.64, "word": " اللي", "probability": 0.721923828125}, {"start": 981.64, "end": 982.5, "word": " متولدة", "probability": 0.94775390625}, {"start": 982.5, "end": 982.76, "word": " من", "probability": 0.99462890625}, {"start": 982.76, "end": 982.94, "word": " ال", "probability": 0.9423828125}, {"start": 982.94, "end": 983.6, "word": " sequence", "probability": 0.97705078125}, {"start": 983.6, "end": 984.78, "word": " سالب", "probability": 0.673583984375}, {"start": 984.78, "end": 985.18, "word": " واحد", "probability": 0.97509765625}, {"start": 985.18, "end": 985.38, "word": " to", "probability": 0.9365234375}, {"start": 985.38, "end": 985.76, "word": " end", "probability": 0.76953125}, {"start": 985.76, "end": 989.84, "word": " اللي", "probability": 0.918212890625}, {"start": 989.84, "end": 990.28, "word": " هي", "probability": 0.82080078125}, {"start": 990.28, "end": 991.76, "word": " أول", "probability": 0.75048828125}, {"start": 991.76, "end": 992.08, "word": " حد", "probability": 0.978515625}, {"start": 992.08, "end": 992.7, "word": " هيكون", "probability": 0.943115234375}, {"start": 992.7, "end": 993.42, "word": " واحد", "probability": 0.976318359375}, {"start": 993.42, "end": 995.12, "word": " بعدين", "probability": 0.8330078125}, {"start": 995.12, "end": 995.64, "word": " سالب", "probability": 0.9694010416666666}, {"start": 995.64, "end": 996.08, "word": " واحد", "probability": 0.978515625}, {"start": 996.08, "end": 996.58, "word": " بعدين", "probability": 0.841552734375}, {"start": 996.58, "end": 997.1, "word": " واحد", "probability": 0.986328125}, {"start": 997.1, "end": 998.5, "word": " بعدين", "probability": 0.908447265625}, {"start": 998.5, "end": 998.96, "word": " سالب", "probability": 0.9830729166666666}, {"start": 998.96, "end": 999.34, "word": " واحد", "probability": 0.989990234375}, {"start": 999.34, "end": 999.54, "word": " و", "probability": 0.83056640625}, {"start": 999.54, "end": 1000.0, "word": " هكذا", "probability": 0.8655598958333334}], "temperature": 1.0}, {"id": 37, "seek": 102860, "start": 1001.61, "end": 1028.61, "text": "show that this series diverges تعالى نشوف ال sequence of partial sums ناخد ال sequence of partial sums والله ده طلعت ال sequence of partial sums convergent بيكون ال series convergent وال sum تبعها بيساوي ال limit", "tokens": [34436, 300, 341, 2638, 18558, 2880, 37279, 6027, 7578, 8717, 8592, 38688, 2423, 8310, 295, 14641, 34499, 8717, 47283, 3215, 2423, 8310, 295, 14641, 34499, 16070, 43761, 11778, 3224, 23032, 1211, 34268, 2423, 8310, 295, 14641, 34499, 9652, 6930, 4724, 1829, 30544, 2423, 2638, 9652, 6930, 16070, 2408, 6055, 3555, 3615, 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0.9541015625}, {"start": 1016.87, "end": 1017.21, "word": " partial", "probability": 0.93798828125}, {"start": 1017.21, "end": 1017.67, "word": " sums", "probability": 0.96923828125}, {"start": 1017.67, "end": 1019.11, "word": " ناخد", "probability": 0.83447265625}, {"start": 1019.11, "end": 1019.21, "word": " ال", "probability": 0.86767578125}, {"start": 1019.21, "end": 1019.51, "word": " sequence", "probability": 0.97509765625}, {"start": 1019.51, "end": 1019.77, "word": " of", "probability": 0.923828125}, {"start": 1019.77, "end": 1020.11, "word": " partial", "probability": 0.94482421875}, {"start": 1020.11, "end": 1020.49, "word": " sums", "probability": 0.93505859375}, {"start": 1020.49, "end": 1020.87, "word": " والله", "probability": 0.755615234375}, {"start": 1020.87, "end": 1021.05, "word": " ده", "probability": 0.81201171875}, {"start": 1021.05, "end": 1021.57, "word": " طلعت", "probability": 0.955078125}, {"start": 1021.57, "end": 1022.49, "word": " ال", "probability": 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"probability": 0.895751953125}, {"start": 1040.83, "end": 1041.57, "word": " لذا", "probability": 0.4581298828125}, {"start": 1041.57, "end": 1041.75, "word": " هنا", "probability": 0.93359375}, {"start": 1041.75, "end": 1042.47, "word": " هنفحص", "probability": 0.84560546875}, {"start": 1042.47, "end": 1043.73, "word": " هل", "probability": 0.9560546875}, {"start": 1043.73, "end": 1044.03, "word": " ال", "probability": 0.94677734375}, {"start": 1044.03, "end": 1044.35, "word": " sequence", "probability": 0.98046875}, {"start": 1044.35, "end": 1044.65, "word": " of", "probability": 0.98046875}, {"start": 1044.65, "end": 1045.03, "word": " partial", "probability": 0.943359375}, {"start": 1045.03, "end": 1045.43, "word": " sums", "probability": 0.9443359375}, {"start": 1045.43, "end": 1046.15, "word": " divergent", "probability": 0.7322998046875}, {"start": 1046.15, "end": 1046.33, "word": " ولا", "probability": 0.74267578125}, {"start": 1046.33, "end": 1048.49, "word": " convergent", "probability": 0.9326171875}, {"start": 1048.49, "end": 1049.09, "word": " طيب", "probability": 0.9298502604166666}, {"start": 1049.09, "end": 1049.41, "word": " تعالوا", "probability": 0.9158528645833334}, {"start": 1049.41, "end": 1049.89, "word": " نفحص", "probability": 0.992431640625}, {"start": 1049.89, "end": 1050.49, "word": " Sn", "probability": 0.487548828125}, {"start": 1050.49, "end": 1051.05, "word": " ال", "probability": 0.533203125}, {"start": 1051.05, "end": 1051.23, "word": " N", "probability": 0.323486328125}, {"start": 1051.23, "end": 1051.39, "word": " في", "probability": 0.9150390625}, {"start": 1051.39, "end": 1051.71, "word": " partial", "probability": 0.935546875}, {"start": 1051.71, "end": 1052.23, "word": " sums", "probability": 0.79345703125}, {"start": 1052.23, "end": 1053.15, "word": " هذا", "probability": 0.5009765625}, {"start": 1053.15, "end": 1053.59, "word": " summation", "probability": 0.7275390625}, {"start": 1053.59, "end": 1054.29, "word": " من", "probability": 0.97900390625}, {"start": 1054.29, "end": 1054.75, "word": " K", "probability": 0.45654296875}, {"start": 1054.75, "end": 1055.31, "word": " equal", "probability": 0.395751953125}, {"start": 1055.31, "end": 1056.03, "word": " 0", "probability": 0.394775390625}, {"start": 1056.03, "end": 1057.19, "word": " to", "probability": 0.9013671875}, {"start": 1057.19, "end": 1057.49, "word": " N", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 39, "seek": 108676, "start": 1059.24, "end": 1086.76, "text": "لا سالب واحد plus k هذا xk فهذا هيطلع الو قيمتين الو هيطلع قيمتين لو كان in even", "tokens": [15040, 8608, 6027, 3555, 36764, 24401, 1804, 350, 23758, 2031, 74, 6156, 3224, 15730, 39896, 9566, 1211, 3615, 2423, 2407, 12174, 32640, 2655, 9957, 2423, 2407, 39896, 9566, 1211, 3615, 12174, 32640, 2655, 9957, 45164, 25961, 294, 754], "avg_logprob": -0.25781248930173045, "compression_ratio": 1.368421052631579, "no_speech_prob": 0.0, "words": [{"start": 1059.24, "end": 1059.6, "word": "لا", "probability": 0.474609375}, {"start": 1059.6, "end": 1060.28, "word": " سالب", "probability": 0.86376953125}, {"start": 1060.28, "end": 1060.84, "word": " واحد", "probability": 0.9755859375}, {"start": 1060.84, "end": 1061.22, "word": " plus", "probability": 0.1448974609375}, {"start": 1061.22, "end": 1061.54, "word": " k", "probability": 0.263427734375}, {"start": 1061.54, "end": 1062.78, "word": " هذا", "probability": 0.765625}, {"start": 1062.78, "end": 1063.58, "word": " xk", "probability": 0.76220703125}, {"start": 1063.58, "end": 1066.32, "word": " فهذا", "probability": 0.9640299479166666}, {"start": 1066.32, "end": 1067.9, "word": " هيطلع", "probability": 0.893310546875}, {"start": 1067.9, "end": 1069.98, "word": " الو", "probability": 0.35491943359375}, {"start": 1069.98, "end": 1070.66, "word": " قيمتين", "probability": 0.90478515625}, {"start": 1070.66, "end": 1072.94, "word": " الو", "probability": 0.81396484375}, {"start": 1072.94, "end": 1073.56, "word": " هيطلع", "probability": 0.9515380859375}, {"start": 1073.56, "end": 1077.3, "word": " قيمتين", "probability": 0.9923095703125}, {"start": 1077.3, "end": 1085.3, "word": " لو", "probability": 0.87255859375}, {"start": 1085.3, "end": 1085.86, "word": " كان", "probability": 0.99560546875}, {"start": 1085.86, "end": 1086.28, "word": " in", "probability": 0.50048828125}, {"start": 1086.28, "end": 1086.76, "word": " even", "probability": 0.9033203125}], "temperature": 1.0}, {"id": 40, "seek": 111165, "start": 1088.35, "end": 1111.65, "text": "أو n odd لو كانت n even يعني نفر بأن n بساوي سفر إذن هيطلع واحد، n بساوي اتنين، هيطلع اندي تلت حدود، مجموعهم برضه واحد، و هكذا، إذن المجموع هذا هيطلع واحد", "tokens": [10721, 2407, 297, 7401, 45164, 25961, 2655, 297, 754, 37495, 22653, 8717, 5172, 2288, 4724, 33456, 297, 4724, 3794, 995, 45865, 8608, 5172, 2288, 11933, 8848, 1863, 39896, 9566, 1211, 3615, 36764, 24401, 12399, 297, 4724, 3794, 995, 45865, 1975, 2655, 1863, 9957, 12399, 39896, 9566, 1211, 3615, 16472, 16254, 6055, 1211, 2655, 11331, 3215, 23328, 12399, 3714, 7435, 2304, 45367, 16095, 4724, 43042, 3224, 36764, 24401, 12399, 4032, 8032, 4117, 15730, 12399, 11933, 8848, 1863, 9673, 7435, 2304, 45367, 23758, 39896, 9566, 1211, 3615, 36764, 24401], "avg_logprob": -0.2681107876653021, "compression_ratio": 1.7549668874172186, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1088.35, "end": 1088.79, "word": "أو", "probability": 0.627685546875}, {"start": 1088.79, "end": 1089.09, "word": " n", "probability": 0.39306640625}, {"start": 1089.09, "end": 1089.63, "word": " odd", "probability": 0.890625}, {"start": 1089.63, "end": 1092.37, "word": " لو", "probability": 0.490966796875}, {"start": 1092.37, "end": 1092.81, "word": " كانت", "probability": 0.97216796875}, {"start": 1092.81, "end": 1093.05, "word": " n", "probability": 0.77685546875}, {"start": 1093.05, "end": 1093.43, "word": " even", "probability": 0.89306640625}, {"start": 1093.43, "end": 1093.71, "word": " يعني", "probability": 0.7666015625}, {"start": 1093.71, "end": 1094.01, "word": " نفر", "probability": 0.452392578125}, {"start": 1094.01, "end": 1094.25, "word": " بأن", "probability": 0.4970703125}, {"start": 1094.25, "end": 1094.59, "word": " n", "probability": 0.394287109375}, {"start": 1094.59, "end": 1095.31, "word": " بساوي", "probability": 0.7213134765625}, {"start": 1095.31, "end": 1096.81, "word": " سفر", "probability": 0.8528645833333334}, {"start": 1096.81, "end": 1098.29, "word": " إذن", "probability": 0.606201171875}, {"start": 1098.29, "end": 1098.75, "word": " هيطلع", "probability": 0.82568359375}, {"start": 1098.75, "end": 1099.69, "word": " واحد،", "probability": 0.6980794270833334}, {"start": 1099.69, "end": 1100.03, "word": " n", "probability": 0.81787109375}, {"start": 1100.03, "end": 1100.53, "word": " بساوي", "probability": 0.8714599609375}, {"start": 1100.53, "end": 1101.55, "word": " اتنين،", "probability": 0.9021484375}, {"start": 1101.55, "end": 1102.47, "word": " هيطلع", "probability": 0.905517578125}, {"start": 1102.47, "end": 1102.73, "word": " اندي", "probability": 0.636474609375}, {"start": 1102.73, "end": 1103.01, "word": " تلت", "probability": 0.8806966145833334}, {"start": 1103.01, "end": 1104.13, "word": " حدود،", "probability": 0.928466796875}, {"start": 1104.13, "end": 1104.79, "word": " مجم��عهم", "probability": 0.9123046875}, {"start": 1104.79, "end": 1105.35, "word": " برضه", "probability": 0.98876953125}, {"start": 1105.35, "end": 1107.29, "word": " واحد،", "probability": 0.8702799479166666}, {"start": 1107.29, "end": 1107.91, "word": " و", "probability": 0.61181640625}, {"start": 1107.91, "end": 1109.07, "word": " هكذا،", "probability": 0.7593994140625}, {"start": 1109.07, "end": 1109.47, "word": " إذن", "probability": 0.8053385416666666}, {"start": 1109.47, "end": 1110.27, "word": " المجموع", "probability": 0.929931640625}, {"start": 1110.27, "end": 1110.57, "word": " هذا", "probability": 0.767578125}, {"start": 1110.57, "end": 1111.03, "word": " هيطلع", "probability": 0.983642578125}, {"start": 1111.03, "end": 1111.65, "word": " واحد", "probability": 0.994384765625}], "temperature": 1.0}, {"id": 41, "seek": 111930, "start": 1112.6, "end": 1119.3, "text": "إذا كانت ال in even أما لو كانت ال in odd يعني لو أخدت in بالساوية واحد", "tokens": [28814, 15730, 25961, 2655, 2423, 294, 754, 5551, 15042, 45164, 25961, 2655, 2423, 294, 7401, 37495, 22653, 45164, 5551, 9778, 3215, 2655, 294, 20666, 3794, 995, 2407, 10632, 36764, 24401], "avg_logprob": -0.21748991743210824, "compression_ratio": 1.2417582417582418, "no_speech_prob": 0.0, "words": [{"start": 1112.6, "end": 1112.94, "word": "إذا", "probability": 0.7069091796875}, {"start": 1112.94, "end": 1113.46, "word": " كانت", "probability": 0.95703125}, {"start": 1113.46, "end": 1113.56, "word": " ال", "probability": 0.93212890625}, {"start": 1113.56, "end": 1113.74, "word": " in", "probability": 0.298583984375}, {"start": 1113.74, "end": 1114.12, "word": " even", "probability": 0.76416015625}, {"start": 1114.12, "end": 1114.98, "word": " أما", "probability": 0.793212890625}, {"start": 1114.98, "end": 1115.16, "word": " لو", "probability": 0.93115234375}, {"start": 1115.16, "end": 1115.52, "word": " كانت", "probability": 0.976806640625}, {"start": 1115.52, "end": 1115.66, "word": " ال", "probability": 0.94189453125}, {"start": 1115.66, "end": 1115.86, "word": " in", "probability": 0.939453125}, {"start": 1115.86, "end": 1116.34, "word": " odd", "probability": 0.85302734375}, {"start": 1116.34, "end": 1117.56, "word": " يعني", "probability": 0.853271484375}, {"start": 1117.56, "end": 1117.7, "word": " لو", "probability": 0.9560546875}, {"start": 1117.7, "end": 1118.1, "word": " أخدت", "probability": 0.9505615234375}, {"start": 1118.1, "end": 1118.26, "word": " in", "probability": 0.89599609375}, {"start": 1118.26, "end": 1118.78, "word": " بالساوية", "probability": 0.6171875}, {"start": 1118.78, "end": 1119.3, "word": " واحد", "probability": 0.954345703125}], "temperature": 1.0}, {"id": 42, "seek": 114292, "start": 1120.4, "end": 1142.92, "text": "لو أخدت in بالساوية واحد فهيطلع عندي حدين مجموعهم سفر لو أخدت in بالساوية تلاتة هيطلع مجموع أول أربع حدود برضه بيطلع مجموعهم سفر و هكذا اذا سفر ال in partial sums بساوية سفر اذا كانت in odd واحد اذا كانت in even وبالتالي therefore", "tokens": [1211, 2407, 5551, 9778, 3215, 2655, 294, 20666, 3794, 995, 2407, 10632, 36764, 24401, 6156, 3224, 1829, 9566, 1211, 3615, 18871, 16254, 11331, 3215, 9957, 3714, 7435, 2304, 45367, 16095, 8608, 5172, 2288, 45164, 5551, 9778, 3215, 2655, 294, 20666, 3794, 995, 2407, 10632, 6055, 1211, 9307, 3660, 39896, 9566, 1211, 3615, 3714, 7435, 2304, 45367, 5551, 12610, 5551, 25513, 3615, 11331, 3215, 23328, 4724, 43042, 3224, 4724, 1829, 9566, 1211, 3615, 3714, 7435, 2304, 45367, 16095, 8608, 5172, 2288, 4032, 8032, 4117, 15730, 1975, 15730, 8608, 5172, 2288, 2423, 294, 14641, 34499, 4724, 3794, 995, 2407, 10632, 8608, 5172, 2288, 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0.74677734375}, {"start": 1137.4, "end": 1137.78, "word": " سفر", "probability": 0.9890950520833334}, {"start": 1137.78, "end": 1137.96, "word": " اذا", "probability": 0.7294921875}, {"start": 1137.96, "end": 1138.4, "word": " كانت", "probability": 0.886962890625}, {"start": 1138.4, "end": 1138.64, "word": " in", "probability": 0.9443359375}, {"start": 1138.64, "end": 1139.06, "word": " odd", "probability": 0.91015625}, {"start": 1139.06, "end": 1139.96, "word": " واحد", "probability": 0.828369140625}, {"start": 1139.96, "end": 1140.16, "word": " اذا", "probability": 0.953857421875}, {"start": 1140.16, "end": 1140.6, "word": " كانت", "probability": 0.96142578125}, {"start": 1140.6, "end": 1140.8, "word": " in", "probability": 0.95166015625}, {"start": 1140.8, "end": 1141.28, "word": " even", "probability": 0.939453125}, {"start": 1141.28, "end": 1142.48, "word": " وبالتالي", "probability": 0.8333333333333334}, {"start": 1142.48, "end": 1142.92, "word": " therefore", "probability": 0.884765625}], "temperature": 1.0}, {"id": 43, "seek": 116971, "start": 1144.21, "end": 1169.71, "text": "therefore a sequence of partial sums is an alternating series يعني حدودها متدبدة بين صفر و واحد أو أول حد واحد التاني صفر واحد صفر و هكذا which is divergent هذه أمرها ما كانت convergent", "tokens": [15456, 845, 257, 8310, 295, 14641, 34499, 307, 364, 40062, 2638, 37495, 22653, 11331, 3215, 23328, 11296, 44650, 3215, 44510, 3660, 49374, 20328, 5172, 2288, 4032, 36764, 24401, 34051, 5551, 12610, 11331, 3215, 36764, 24401, 16712, 7649, 1829, 20328, 5172, 2288, 36764, 24401, 20328, 5172, 2288, 4032, 8032, 4117, 15730, 597, 307, 18558, 6930, 29538, 5551, 29973, 11296, 19446, 25961, 2655, 9652, 6930], "avg_logprob": -0.27148436615243554, "compression_ratio": 1.449438202247191, "no_speech_prob": 0.0, "words": [{"start": 1144.21, "end": 1145.13, "word": "therefore", "probability": 0.49627685546875}, {"start": 1145.13, "end": 1145.65, "word": " a", "probability": 0.2020263671875}, {"start": 1145.65, "end": 1146.25, "word": " sequence", "probability": 0.96484375}, {"start": 1146.25, "end": 1146.55, "word": " of", "probability": 0.96630859375}, {"start": 1146.55, "end": 1147.03, "word": " partial", "probability": 0.9306640625}, {"start": 1147.03, "end": 1147.53, "word": " sums", "probability": 0.9619140625}, {"start": 1147.53, "end": 1148.63, "word": " is", "probability": 0.93408203125}, {"start": 1148.63, "end": 1149.09, "word": " an", "probability": 0.7802734375}, {"start": 1149.09, "end": 1149.87, "word": " alternating", "probability": 0.9677734375}, {"start": 1149.87, "end": 1151.11, "word": " series", "probability": 0.88525390625}, {"start": 1151.11, "end": 1152.09, "word": " يعني", "probability": 0.53509521484375}, {"start": 1152.09, "end": 1152.47, "word": " حدودها", "probability": 0.96044921875}, {"start": 1152.47, "end": 1153.05, "word": " متدبدة", "probability": 0.77203369140625}, {"start": 1153.05, "end": 1153.39, "word": " بين", "probability": 0.63134765625}, {"start": 1153.39, "end": 1153.81, "word": " صفر", "probability": 0.8460286458333334}, {"start": 1153.81, "end": 1153.93, "word": " و", "probability": 0.89501953125}, {"start": 1153.93, "end": 1154.29, "word": " واحد", "probability": 0.95947265625}, {"start": 1154.29, "end": 1154.95, "word": " أو", "probability": 0.51806640625}, {"start": 1154.95, "end": 1155.43, "word": " أول", "probability": 0.823974609375}, {"start": 1155.43, "end": 1155.75, "word": " حد", "probability": 0.987548828125}, {"start": 1155.75, "end": 1156.17, "word": " واحد", "probability": 0.94482421875}, {"start": 1156.17, "end": 1156.63, "word": " التاني", "probability": 0.76220703125}, {"start": 1156.63, "end": 1157.15, "word": " صفر", "probability": 0.96630859375}, {"start": 1157.15, "end": 1158.29, "word": " واحد", "probability": 0.904296875}, {"start": 1158.29, "end": 1158.93, "word": " صفر", "probability": 0.927734375}, {"start": 1158.93, "end": 1160.03, "word": " و", "probability": 0.59375}, {"start": 1160.03, "end": 1160.61, "word": " هكذا", "probability": 0.8982747395833334}, {"start": 1160.61, "end": 1163.71, "word": " which", "probability": 0.9267578125}, {"start": 1163.71, "end": 1164.43, "word": " is", "probability": 0.97021484375}, {"start": 1164.43, "end": 1165.57, "word": " divergent", "probability": 0.815673828125}, {"start": 1165.57, "end": 1168.05, "word": " هذه", "probability": 0.09197998046875}, {"start": 1168.05, "end": 1168.45, "word": " أمرها", "probability": 0.8800455729166666}, {"start": 1168.45, "end": 1168.59, "word": " ما", "probability": 0.72802734375}, {"start": 1168.59, "end": 1168.95, "word": " كانت", "probability": 0.8994140625}, {"start": 1168.95, "end": 1169.71, "word": " convergent", "probability": 0.830078125}], "temperature": 1.0}, {"id": 44, "seek": 119833, "start": 1173.47, "end": 1198.33, "text": "الـ sequence هذه divergent عارفين ليه؟ لأن هي ال proof الـ subsequence الحدود مثلا الزوجية S2K", "tokens": [6027, 39184, 8310, 29538, 18558, 6930, 6225, 9640, 5172, 9957, 32239, 3224, 22807, 5296, 33456, 39896, 2423, 8177, 2423, 39184, 13924, 655, 2423, 24401, 23328, 50113, 15040, 6024, 110, 29245, 10632, 318, 17, 42], "avg_logprob": -0.27299107483455115, "compression_ratio": 1.1322314049586777, "no_speech_prob": 0.0, "words": [{"start": 1173.47, "end": 1174.11, "word": "الـ", "probability": 0.432373046875}, {"start": 1174.11, "end": 1174.49, "word": " sequence", "probability": 0.84716796875}, {"start": 1174.49, "end": 1174.81, "word": " هذه", "probability": 0.57568359375}, {"start": 1174.81, "end": 1175.59, "word": " divergent", "probability": 0.614990234375}, {"start": 1175.59, "end": 1177.09, "word": " عارفين", "probability": 0.9267578125}, {"start": 1177.09, "end": 1178.33, "word": " ليه؟", "probability": 0.873046875}, {"start": 1178.33, "end": 1178.73, "word": " لأن", "probability": 0.878662109375}, {"start": 1178.73, "end": 1179.03, "word": " هي", "probability": 0.349853515625}, {"start": 1179.03, "end": 1179.27, "word": " ال", "probability": 0.826171875}, {"start": 1179.27, "end": 1179.65, "word": " proof", "probability": 0.935546875}, {"start": 1179.65, "end": 1182.49, "word": " الـ", "probability": 0.4923095703125}, {"start": 1182.49, "end": 1183.43, "word": " subsequence", "probability": 0.932861328125}, {"start": 1183.43, "end": 1194.13, "word": " الحدود", "probability": 0.8248697916666666}, {"start": 1194.13, "end": 1194.59, "word": " مثلا", "probability": 0.97900390625}, {"start": 1194.59, "end": 1195.45, "word": " الزوجية", "probability": 0.91748046875}, {"start": 1195.45, "end": 1198.33, "word": " S2K", "probability": 0.7652994791666666}], "temperature": 1.0}, {"id": 45, "seek": 123096, "start": 1203.52, "end": 1230.96, "text": "هي أول حد وهي التاني لإن الحدود الزوجية أصفار كلهم صح؟ تكون بيرجل سفر and ال subsequence التانية اللي حدودها فردية كلهم واحد، ثابت واحد وهدي تكون بيرجل واحد نعم؟", "tokens": [3224, 1829, 5551, 12610, 11331, 3215, 37037, 1829, 16712, 7649, 1829, 5296, 28814, 1863, 21542, 3215, 23328, 6024, 110, 29245, 10632, 5551, 9381, 5172, 9640, 28242, 16095, 20328, 5016, 22807, 6055, 30544, 4724, 1829, 47341, 1211, 8608, 5172, 2288, 293, 2423, 13924, 655, 16712, 7649, 10632, 13672, 1829, 11331, 3215, 23328, 11296, 6156, 2288, 3215, 10632, 28242, 16095, 36764, 24401, 12399, 38637, 16758, 2655, 36764, 24401, 37037, 16254, 6055, 30544, 4724, 1829, 47341, 1211, 36764, 24401, 8717, 25957, 22807], "avg_logprob": -0.22109375055879354, "compression_ratio": 1.680722891566265, "no_speech_prob": 0.0, "words": [{"start": 1203.52, "end": 1203.82, "word": "هي", "probability": 0.7080078125}, {"start": 1203.82, "end": 1204.2, "word": " أول", "probability": 0.909423828125}, {"start": 1204.2, "end": 1204.62, "word": " حد", "probability": 0.992431640625}, {"start": 1204.62, "end": 1205.28, "word": " وهي", "probability": 0.5545654296875}, {"start": 1205.28, "end": 1205.84, "word": " التاني", "probability": 0.8055013020833334}, {"start": 1205.84, "end": 1206.6, "word": " لإن", "probability": 0.6482747395833334}, {"start": 1206.6, "end": 1206.98, "word": " الحدود", "probability": 0.9752604166666666}, {"start": 1206.98, "end": 1207.66, "word": " الزوجية", "probability": 0.96728515625}, {"start": 1207.66, "end": 1208.32, "word": " أصفار", "probability": 0.844482421875}, {"start": 1208.32, "end": 1208.76, "word": " كلهم", "probability": 0.9658203125}, {"start": 1208.76, "end": 1210.64, "word": " صح؟", "probability": 0.798828125}, {"start": 1210.64, "end": 1210.74, "word": " تكون", "probability": 0.5699462890625}, {"start": 1210.74, "end": 1211.2, "word": " بيرجل", "probability": 0.67840576171875}, {"start": 1211.2, "end": 1211.68, "word": " سفر", "probability": 0.9318033854166666}, {"start": 1211.68, "end": 1213.32, "word": " and", "probability": 0.6650390625}, {"start": 1213.32, "end": 1214.64, "word": " ال", "probability": 0.9052734375}, {"start": 1214.64, "end": 1215.52, "word": " subsequence", "probability": 0.69775390625}, {"start": 1215.52, "end": 1216.2, "word": " التانية", "probability": 0.9698893229166666}, {"start": 1216.2, "end": 1217.12, "word": " اللي", "probability": 0.7177734375}, {"start": 1217.12, "end": 1217.68, "word": " حدودها", "probability": 0.992919921875}, {"start": 1217.68, "end": 1218.32, "word": " فردية", "probability": 0.9346923828125}, {"start": 1218.32, "end": 1223.4, "word": " كلهم", "probability": 0.946533203125}, {"start": 1223.4, "end": 1224.54, "word": " واحد،", "probability": 0.8753255208333334}, {"start": 1224.54, "end": 1225.06, "word": " ثابت", "probability": 0.9225260416666666}, {"start": 1225.06, "end": 1225.5, "word": " واحد", "probability": 0.99267578125}, {"start": 1225.5, "end": 1226.38, "word": " وهدي", "probability": 0.34375}, {"start": 1226.38, "end": 1226.58, "word": " تكون", "probability": 0.94482421875}, {"start": 1226.58, "end": 1227.1, "word": " بيرجل", "probability": 0.872802734375}, {"start": 1227.1, "end": 1227.66, "word": " واحد", "probability": 0.984130859375}, {"start": 1227.66, "end": 1230.96, "word": " نعم؟", "probability": 0.853515625}], "temperature": 1.0}, {"id": 46, "seek": 125040, "start": 1231.6, "end": 1250.4, "text": "وبالتالي إذا مادام في عندي two subsequences واحدة converge لصفر وواحدة converge لواحد وصفر بيسويش الواحد وصفر لا يساوي الواحد معناته by the divergence criterion ال sequence هذه is divergent", "tokens": [37746, 6027, 2655, 6027, 1829, 11933, 15730, 3714, 18513, 10943, 8978, 18871, 16254, 732, 13924, 2667, 36764, 24401, 3660, 41881, 5296, 9381, 5172, 2288, 4032, 14407, 24401, 3660, 41881, 5296, 14407, 24401, 4032, 9381, 5172, 2288, 4724, 1829, 3794, 45865, 8592, 2423, 14407, 24401, 4032, 9381, 5172, 2288, 20193, 7251, 3794, 995, 45865, 2423, 14407, 24401, 20449, 8315, 47395, 538, 264, 47387, 46691, 2423, 8310, 29538, 307, 18558, 6930], "avg_logprob": -0.23482143133878708, "compression_ratio": 1.6369047619047619, "no_speech_prob": 0.0, "words": [{"start": 1231.6, "end": 1233.02, "word": "وبالتالي", "probability": 0.93427734375}, {"start": 1233.02, "end": 1233.62, "word": " إذا", "probability": 0.7164306640625}, {"start": 1233.62, "end": 1234.32, "word": " مادام", "probability": 0.5056966145833334}, {"start": 1234.32, "end": 1234.5, "word": " في", "probability": 0.460693359375}, {"start": 1234.5, "end": 1234.76, "word": " عندي", "probability": 0.73779296875}, {"start": 1234.76, "end": 1234.92, "word": " two", "probability": 0.74755859375}, {"start": 1234.92, "end": 1235.78, "word": " subsequences", "probability": 0.864013671875}, {"start": 1235.78, "end": 1236.18, "word": " واحدة", "probability": 0.9049479166666666}, {"start": 1236.18, "end": 1236.6, "word": " converge", "probability": 0.78564453125}, {"start": 1236.6, "end": 1237.12, "word": " لصفر", "probability": 0.75677490234375}, {"start": 1237.12, "end": 1237.54, "word": " وواحدة", "probability": 0.8253173828125}, {"start": 1237.54, "end": 1237.92, "word": " converge", "probability": 0.72314453125}, {"start": 1237.92, "end": 1238.52, "word": " لواحد", "probability": 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"probability": 0.333740234375}, {"start": 1247.74, "end": 1248.84, "word": " ال", "probability": 0.79736328125}, {"start": 1248.84, "end": 1249.2, "word": " sequence", "probability": 0.94970703125}, {"start": 1249.2, "end": 1249.54, "word": " هذه", "probability": 0.393798828125}, {"start": 1249.54, "end": 1249.66, "word": " is", "probability": 0.75146484375}, {"start": 1249.66, "end": 1250.4, "word": " divergent", "probability": 0.87060546875}], "temperature": 1.0}, {"id": 47, "seek": 127713, "start": 1251.89, "end": 1277.13, "text": "لأن لو كانت ال sequence هذي convergent فمفروض أي subsequence تكون convergent لنفس ال limit يعني المفروض دول ال limits تكون متساويين و هذا مستحيل إذا ال sequence of partial sums هنا divergent وبالتالي نكمل الحل هنا و بالتالي therefore the series", "tokens": [1211, 33456, 45164, 25961, 2655, 2423, 8310, 8032, 8848, 1829, 9652, 6930, 6156, 2304, 5172, 32887, 11242, 36632, 13924, 655, 6055, 30544, 9652, 6930, 5296, 1863, 36178, 2423, 4948, 37495, 22653, 9673, 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"word": " الحد", "probability": 0.98779296875}, {"start": 1567.27, "end": 1567.73, "word": " البعد", "probability": 0.63671875}, {"start": 1567.73, "end": 1567.89, "word": " و", "probability": 0.82080078125}, {"start": 1567.89, "end": 1568.29, "word": " نص", "probability": 0.780517578125}, {"start": 1568.29, "end": 1570.01, "word": " سالب", "probability": 0.97314453125}, {"start": 1570.01, "end": 1570.69, "word": " تلت", "probability": 0.9733072916666666}, {"start": 1570.69, "end": 1572.09, "word": " و", "probability": 0.5810546875}, {"start": 1572.09, "end": 1572.77, "word": " هكذا", "probability": 0.9265950520833334}, {"start": 1572.77, "end": 1574.67, "word": " إلى", "probability": 0.76806640625}, {"start": 1574.67, "end": 1575.35, "word": " الحد", "probability": 0.993896484375}, {"start": 1575.35, "end": 1576.01, "word": " الأخير", "probability": 0.9295247395833334}, {"start": 1576.01, "end": 1576.65, "word": " هيكون", "probability": 0.8193359375}, {"start": 1576.65, "end": 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هذا بيروح مع سالب واحد على ان في الحد اللي يصدقه مباشرة", "tokens": [3555, 1863, 15040, 5016, 19913, 14739, 9673, 7435, 2304, 45367, 23758, 37085, 278, 37495, 22653, 8978, 11331, 3215, 23328, 8978, 11296, 11933, 11622, 47302, 6055, 2655, 1211, 33599, 7578, 20449, 21542, 3215, 23328, 13672, 1829, 45030, 16254, 11296, 37495, 22653, 8608, 6027, 3555, 8717, 9381, 20193, 5016, 19913, 14407, 4724, 13546, 2407, 5016, 20449, 3714, 29245, 3555, 8717, 9381, 46952, 6027, 3555, 6055, 1211, 2655, 39896, 32887, 5016, 20449, 3714, 29245, 3555, 6055, 1211, 2655, 8978, 21542, 3215, 13672, 1829, 7251, 20292, 3224, 3714, 3555, 33599, 25720, 4032, 14407, 24401, 15844, 16472, 23758, 4724, 13546, 2407, 5016, 20449, 8608, 6027, 3555, 36764, 24401, 15844, 16472, 8978, 21542, 3215, 13672, 1829, 7251, 9381, 3215, 4587, 3224, 3714, 3555, 33599, 25720], "avg_logprob": -0.13359375496705372, "compression_ratio": 2.1557788944723617, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1582.84, "end": 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بساوي واحد اللي هو limit لل sequence of partial sums تمام؟ إذا هذا النوع من ال series بنسميه telescoping .. telescoping .. telescoping series", "tokens": [474, 2423, 2408, 6055, 3555, 3615, 11296, 37495, 22653, 3714, 7435, 2304, 45367, 11296, 4724, 3794, 995, 45865, 36764, 24401, 13672, 1829, 31439, 4948, 24976, 8310, 295, 14641, 34499, 46811, 10943, 22807, 11933, 15730, 23758, 28239, 45367, 9154, 2423, 2638, 44945, 38251, 1829, 3224, 37085, 278, 4386, 37085, 278, 4386, 37085, 278, 2638], "avg_logprob": -0.24956596394379935, "compression_ratio": 1.4591194968553458, "no_speech_prob": 0.0, "words": [{"start": 1683.72, "end": 1684.4, "word": "and", "probability": 0.1788330078125}, {"start": 1684.4, "end": 1685.4, "word": " ال", "probability": 0.47998046875}, {"start": 1685.4, "end": 1685.66, "word": " sum", "probability": 0.75537109375}, {"start": 1685.66, "end": 1686.32, "word": " تبعها", "probability": 0.9208984375}, {"start": 1686.32, "end": 1686.8, "word": " يعني", "probability": 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"probability": 0.813232421875}, {"start": 1705.22, "end": 1708.14, "word": " series", "probability": 0.92626953125}], "temperature": 1.0}, {"id": 64, "seek": 172111, "start": 1711.71, "end": 1721.11, "text": "such type of series is called telescoping series okay تمام واضح", "tokens": [39974, 2010, 295, 2638, 307, 1219, 37085, 278, 2638, 1392, 46811, 10943, 4032, 46958, 5016], "avg_logprob": -0.2714843675494194, "compression_ratio": 0.9594594594594594, "no_speech_prob": 0.0, "words": [{"start": 1711.71, "end": 1712.35, "word": "such", "probability": 0.55029296875}, {"start": 1712.35, "end": 1713.41, "word": " type", "probability": 0.96533203125}, {"start": 1713.41, "end": 1713.69, "word": " of", "probability": 0.96826171875}, {"start": 1713.69, "end": 1714.27, "word": " series", "probability": 0.9462890625}, {"start": 1714.27, "end": 1715.11, "word": " is", "probability": 0.9638671875}, {"start": 1715.11, "end": 1715.47, "word": " called", "probability": 0.92041015625}, {"start": 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\ No newline at end of file