Chapter 11.3, Problem 37E

(a) Use the sum of the first 10 terms to estimate the sum of the series ${\displaystyle {\sum }_{n-1}^{\infty }1}/n^2$. How good is this estimate?

(b) Improve this estimate using (3) with $n=0$.

(c) Compare your estimate in part (b) with the exact value given in Exercise 34.

(d) Find a value of n that will ensure that the error in the approximation $s\approx s_n$ is less than 0.001.