Series Convergence and Divergence

1. The problem statement, all variables and given/known data
Determine if the following series converges or diverges. If it converges determine its sum.
Ʃ1/(i²-1) where the upper limit is n and the index i=2


2. Relevant equations

The General Formula for the partial sum was given:
S_n=Ʃ1/(i²-1)=3/4-1/(2n)-1/(2(n+1)

3. The attempt at a solution
I have no idea where to start. I tried to get the General Formula, but I am really confused as to how to even start. I tried to split the function with partial fractions and somehow got 1/(2(i+1))-1/(2(i-1))

 

oops! I got it. It's a telescopic sum. I need to open my eyes a little more.