Answer
(a) 91
(b) 819
(c) 8281
Work Step by Step
(a) Recall: \begin{equation}\sum_{k=1}^{n}k=\frac{n(n+1)}{2}\end{equation} \begin{equation}\implies\sum_{k=1}^{13}k=\frac{13(13+1)}{2}=91\end{equation}
(b) Recall: \begin{equation}\sum_{k=1}^{n}k^{2}=\frac{n(n+1)(2n+1)}{6}\end{equation} \begin{equation}\implies\sum_{k=1}^{13}k^{2}=\frac{13(13+1)(2\times13+1)}{6}=819\end{equation}
(c) Recall: \begin{equation}\sum_{k=1}^{n}k^{3}=\frac{n^{2}(n+1)^{2}}{4}\end{equation} \begin{equation}\implies\sum_{k=1}^{13}k^{3}=\frac{13^{2}\times(13+1)^{2}}{4}=8281\end{equation}
