Chapter 5 - The Integral - 5.1 Approximating and Computing Area - Exercises - Page 236: 37

1,093,350

\begin{equation} \sum_{n=51}^{150}n^{2}=\sum_{n=1}^{150}n^{2}-\sum_{n=1}^{50}n^{2}\end{equation}\begin{equation}=\frac{150(150+1)(2\times150+1)}{6}-\frac{50(50+1)(2\times50+1)}{6}\end{equation}\begin{equation}=1,093,350 \end{equation}