I have to find the formula for sum $$\sum_{i=2}^{n} \frac1{i^2-1}$$ I remember reading somewhere that $\displaystyle \frac1{i^2-1}$ can be shown as $\displaystyle\frac1{i+1}$ and $\displaystyle \frac1{i-1}$.
If I can express it as this, then I should be able to create a telescopic sum, and produce the formula easily. But how can I get to those two fractions in the first place so that I can build the proof?