Chapter 10.4, Problem 69E

Reciprocals of odd squares Assume that ${\displaystyle \underset{k=1}{\overset{\ne }{\sum }}\frac{1}{k^2}=\frac{{\pi }^2}{6}}$ (Exercises 65 and 66) and that the terms of this series may be rearranged without changing the value of the series. Determine the sum of the reciprocals of the squares of the odd positive integers.