Hello! Here is something that I've been wondering for quite a while. Consider the following two infinite series:

$\displaystyle S = \sum_{k\ge0}\frac{1}{(ak+b)(ck+d)}, ~~ T = \sum_{k\ge0}\frac{(-1)^k}{(ak+b)(ck+d)}$

Assuming that all issues of convergence are sorted, what's the relation (if any) between the values of S and T?