ca.analysis and odes - Evaluation of the following Series

Hi there,

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

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

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/(1cdot2) + 1/(3cdot4) + 1/(5cdot6) + ... 1/(2ncdot(2n-1)) = log(2) $ (Note that ${ntoinfty}$ 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