Answer
a) 55
b) 385
c) 3025
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}^{10}k=\frac{10(10+1)}{2}=55\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}^{10}k^{2}=\frac{10(10+1)(2\times10+1)}{6}=385\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}^{10}k^{3}=\frac{10^{2}\times(10+1)^{2}}{4}=3025\end{equation}
