Sum of (arithmetic?) infinite series How the heck do I find the sum of a series like $\sum\limits_{n=3}^\infty\frac{5}{36n^{2}-9}$? I can't seem to convert this to a geometric series and I don't have a finite number of partial sums, so I'm stumped.

$$\frac{5}{9}\sum \frac{1}{4x^2-1}$$
$$=\frac{5}{18}\sum \frac{1}{2x-1}-\frac{1}{2x+1}$$
$$=\frac{5}{18}[ \frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}...]$$
$$=\frac{5}{18}[\frac{1}{5}]$$
$$=\frac{1}{18}$$
