Thank you for reporting, we will resolve it shortly
Q.
The sum $\displaystyle\sum_{r=2}^{\infty} \frac{1}{r^2-1}$ is equal to
Sequences and Series
Solution:
$S=\displaystyle\sum_{r=2}^{\infty} \frac{1}{r^2-1}=\displaystyle\sum_{r=2}^{\infty} \frac{1}{(r-1)(r+1)}$
$T _{ r }=\frac{1}{( r -1)( r +1)}=\frac{1}{2}\left[\frac{1}{ r -1}-\frac{1}{ r +1}\right] \Rightarrow S _{\infty}=\frac{3}{4}$