Chapter 8.6, Problem 34E

Remainders in alternating series Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than 10⁻⁴ in magnitude. Although you do not need it, the exact value of the series is given in each case.

34. $\frac{{\pi }^2}{32}={\displaystyle \underset{k=0}{\overset{\infty }{\sum }}\frac{{(-1)}^k}{{(2k+1)}^3}}$