Chapter 5 - The Integral - 5.1 Approximating and Computing Area - Exercises - Page 236: 39

41,650

\begin{equation} \sum_{j=0}^{50}j(j-1)=\sum_{j=0}^{50}(j^{2}-j)\end{equation}\begin{equation}=(0^{2}-0)+\sum_{j=1}^{50}(j^{2}-j)\end{equation}\begin{equation}=\sum_{j=1}^{50}j^{2}-\sum_{j=1}^{50}j \end{equation}\begin{equation}=\frac{50(50+1)(2\times50+1)}{6}-\frac{50(50+1)}{2}=41,650\end{equation}