infinite sum 1/ (2p+1)^2 (V Soros Olympiad 1998-99 Round 2 10.2)
Source:
May 25, 2024
algebra
Problem Statement
In , the great Russian mathematician Leonhard Euler published one of his most important works, Introduction to the Analysis of Infinites. In this work, in particular, Euler finds the values of two infinite sums and (the terms in the first sum are the inverses of the squares of the natural numbers, and in the second are the inverses of the squares of the odd numbers of the natural series). The value of the first sum, as Euler proved, equals . Given this result, find the value of the second sum.