Is there a closed-form expression for the sum:
$$ \sum \limits_{i=2}^{n} \frac{1}{i^2-1} $$
Is there a closed-form expression for the sum:
$$ \sum \limits_{i=2}^{n} \frac{1}{i^2-1} $$
Hint $$ \frac{1}{i^2-1}=\frac{1}{2}\left(\frac{1}{i-1}-\frac{1}{i+1}\right) $$ Now use telescopy.
Here is a closed form for the series
$$ -\frac{1}{2}\,{\frac {1+2\,n}{ \left( n+1 \right) n}} + \frac{3}{4} \,. $$