Chapter 5.3, Problem 169E

Use the estimate $R_N\le {\displaystyle {\int }_N^{\infty }f\left(t\right)dt}$to find a bound for the remainder $R_N={\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{a}_n-{\displaystyle \underset{n=1}{\overset{N}{\sum }}{a}_n}}$, where $a_n=f\left(n\right)$.

169. ${\displaystyle \underset{n=1}{\overset{100}{\sum }}\frac{1}{n^2}}$