Question

find the sum of the series... n=1... to infinity.. n/((2n-1)^2)((2n+1)^2)

Answer 1

n/((2n-1)^2)((2n+1)^2) doesn't even converge.
n/(((2n-1)^2)((2n+1)^2)) converges to 1/8.

Answer 2

This basically expands by partial fractions to 1/(8*(2n-1)^2)+1/(8*(2n+1)^2) which telescopes.