# Thread: General formula of a series

1. ## General formula of a series

Hi everyone! I have some problems in understanding the following general formula:
$\displaystyle S_n=\sum_{k=2}^{n} \frac{1}{k^2-1}=\frac{3}{4}-\frac{1}{2n}-\frac{1}{2(n+1)}$
Does anyone have a proof for this? Any effort will be appreciated.

2. Replace $\frac{1}{k^2-1}$ with its partial fraction decomposition, then write out the series term by term. A bunch of stuff should cancel leaving the desired result.