24. $\lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^{n} \sqrt{1 + \frac{3k}{n}}$ 의 값은? [3점]

\begin{itemize}
    \item[1] $\frac{4}{3}$
    \item[2] $\frac{13}{9}$
    \item[3] $\frac{14}{9}$
    \item[4] $\frac{5}{3}$
    \item[5] $\frac{16}{9}$
\end{itemize}