Hi there,

I was wondering if you guys could be able to find the sum of the following series:

$ S = 1/((1\cdot2)^2) + 1/((3\cdot4)^2) + 1/((5\cdot6)^2) + ... + 1/(((2n-1)\cdot2n)^2) $, in which $\{n\to\infty}$ .

This question came to mind when I was looking at this (http://www.stat.purdue.edu/~dasgupta/publications/tr02-03.pdf) paper by Professor Anirban DasGupta. In the last section, a couple of specific examples of his 'unified' method to find the sums of infinite series is pressented. In equation (34), he states that the following series:

$ 1/(1\cdot2) + 1/(3\cdot4) + 1/(5\cdot6) + ... 1/(2n\cdot(2n-1)) = log(2) $ (Note that $\{n\to\infty}$ again). I was wondering If it's possible to find the sum if the values of the denominators of the terms are squared.

Thanks in advance,

Max Muller