{"segments": [{"id": 1, "seek": 3025, "start": 2.33, "end": 30.25, "text": "بسم الله الرحمن الرحيم اليوم ان شاء الله راح نكمل في شبتر عشرة اللي هو عن ال infinite series سبشن عشرة سبعة همنا نحكي اليوم عن ال power series power series بدنا نعرف بالأول إيش هي ال power series طبعا power series إما بتكون حوالين x تساوي سفر أو x تساوي أي نقطة أخرى اللي هي ال a ال power series حوالين x تساوي سفر يعني شكلها بتكون لو صمش ل cn x أس n", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 16472, 13412, 16606, 21984, 12602, 39319, 8717, 24793, 1211, 8978, 13412, 3555, 2655, 2288, 6225, 8592, 25720, 13672, 1829, 31439, 18871, 2423, 13785, 2638, 8608, 3555, 8592, 1863, 6225, 8592, 25720, 8608, 3555, 27884, 8032, 2304, 8315, 8717, 5016, 4117, 1829, 45595, 20498, 18871, 2423, 1347, 2638, 1347, 2638, 47525, 8315, 8717, 3615, 28480, 20666, 10721, 12610, 11933, 1829, 8592, 39896, 2423, 1347, 2638, 23032, 3555, 3615, 995, 1347, 2638, 11933, 15042, 39894, 30544, 11331, 2407, 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converges absolutely طبعا ال series converges absolutely لما ال x ناقص a أقل من r يعني x بين a ناقص a و a ناقص r و a زائد r", "tokens": [1829, 3555, 4587, 7578, 44945, 14851, 9778, 40448, 11296, 281, 915, 264, 15035, 689, 264, 2638, 9652, 2880, 3122, 23032, 3555, 3615, 995, 2423, 2638, 9652, 2880, 3122, 5296, 15042, 2423, 2031, 8717, 995, 4587, 9381, 257, 5551, 4587, 1211, 9154, 367, 37495, 22653, 2031, 49374, 257, 8717, 995, 4587, 9381, 257, 4032, 257, 8717, 995, 4587, 9381, 367, 4032, 257, 30767, 16373, 3215, 367], "avg_logprob": -0.29024620399330603, "compression_ratio": 1.4838709677419355, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 529.79, "end": 530.39, "word": "يبقى", "probability": 0.7440185546875}, {"start": 530.39, "end": 530.99, "word": " بنستخدمها", "probability": 0.705419921875}, {"start": 530.99, "end": 531.11, "word": " to", "probability": 0.282470703125}, {"start": 531.11, "end": 531.39, "word": " find", "probability": 0.904296875}, {"start": 531.39, 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end point اللى باخد النقطة X-R و ببحث عندها series هل هي converge ولا لأ و A زاد R باخدها كمان مرة لحالها و ببحث ال series هل هي converge ولا diverge", "tokens": [6027, 7649, 39182, 39896, 4117, 11778, 38436, 4587, 33599, 5296, 31377, 2304, 33962, 9566, 2407, 3660, 16712, 7649, 10632, 13672, 7578, 31439, 498, 264, 15035, 295, 8236, 32181, 307, 19362, 37495, 22653, 2423, 15035, 8032, 18513, 13672, 7578, 316, 12, 49, 4032, 316, 30767, 18513, 497, 1500, 337, 32181, 420, 47387, 412, 1184, 917, 935, 43242, 28242, 917, 935, 13672, 7578, 4724, 47283, 3215, 28239, 47432, 3660, 1783, 12, 49, 4032, 4724, 49628, 12984, 43242, 11296, 2638, 8032, 1211, 39896, 41881, 49429, 5296, 10721, 4032, 316, 30767, 18513, 497, 4724, 47283, 3215, 11296, 9122, 2304, 7649, 3714, 25720, 5296, 5016, 6027, 11296, 4032, 4724, 49628, 12984, 2423, 2638, 8032, 1211, 39896, 41881, 49429, 18558, 432], "avg_logprob": -0.226562503596832, "compression_ratio": 1.8314176245210727, "no_speech_prob": 1.1920928955078125e-07, 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{"start": 568.49, "end": 568.75, "word": " series", "probability": 0.384033203125}, {"start": 568.75, "end": 568.97, "word": " هل", "probability": 0.9267578125}, {"start": 568.97, "end": 569.05, "word": " هي", "probability": 0.84521484375}, {"start": 569.05, "end": 569.45, "word": " converge", "probability": 0.88037109375}, {"start": 569.45, "end": 569.65, "word": " ولا", "probability": 0.50048828125}, {"start": 569.65, "end": 569.91, "word": " لأ", "probability": 0.786376953125}, {"start": 569.91, "end": 570.35, "word": " و", "probability": 0.921875}, {"start": 570.35, "end": 570.53, "word": " A", "probability": 0.73583984375}, {"start": 570.53, "end": 570.71, "word": " زاد", "probability": 0.89453125}, {"start": 570.71, "end": 570.97, "word": " R", "probability": 0.97265625}, {"start": 570.97, "end": 571.33, "word": " باخدها", "probability": 0.9359130859375}, {"start": 571.33, "end": 571.61, "word": " كمان", "probability": 0.9078776041666666}, {"start": 571.61, "end": 571.85, "word": " مرة", "probability": 0.87109375}, {"start": 571.85, "end": 572.25, "word": " لحالها", "probability": 0.977783203125}, {"start": 572.25, "end": 572.41, "word": " و", "probability": 0.81689453125}, {"start": 572.41, "end": 572.73, "word": " ببحث", "probability": 0.9607747395833334}, {"start": 572.73, "end": 572.85, "word": " ال", "probability": 0.44384765625}, {"start": 572.85, "end": 573.05, "word": " series", "probability": 0.92431640625}, {"start": 573.05, "end": 573.27, "word": " هل", "probability": 0.935546875}, {"start": 573.27, "end": 573.39, "word": " هي", "probability": 0.91162109375}, {"start": 573.39, "end": 573.79, "word": " converge", "probability": 0.97119140625}, {"start": 573.79, "end": 574.11, "word": " ولا", "probability": 0.90380859375}, {"start": 574.11, "end": 575.47, "word": " diverge", "probability": 0.8115234375}], "temperature": 1.0}, {"id": 25, "seek": 59054, "start": 576.09, "end": 590.55, "text": "طبعا في هذه الحالة بنشوف ال series إيش اللي بتطلع معنا إذا كانت series of positive terms قدامي خمسة set أستخدمهم إذا كانت ال series alternating series طبعا بنعرف برضه كيف نفحص ال alternating series", "tokens": [9566, 3555, 3615, 995, 8978, 29538, 21542, 6027, 3660, 44945, 8592, 38688, 2423, 2638, 11933, 1829, 8592, 13672, 1829, 39894, 9566, 1211, 3615, 20449, 8315, 11933, 15730, 25961, 2655, 2638, 295, 3353, 2115, 12174, 3215, 10943, 1829, 16490, 2304, 3794, 3660, 992, 5551, 14851, 9778, 40448, 16095, 11933, 15730, 25961, 2655, 2423, 2638, 40062, 2638, 23032, 3555, 3615, 995, 44945, 3615, 28480, 4724, 43042, 3224, 9122, 33911, 8717, 5172, 5016, 9381, 2423, 40062, 2638], "avg_logprob": -0.17552082657814025, "compression_ratio": 1.5846994535519126, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 576.09, "end": 576.71, "word": "طبعا", "probability": 0.785491943359375}, {"start": 576.71, "end": 576.83, "word": " في", "probability": 0.677734375}, {"start": 576.83, "end": 576.99, "word": " هذه", "probability": 0.84033203125}, {"start": 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