# Finding nth Partial Sum

Can someone tell me how I could find a formula for the nth partial sum of the series by using it to find the series' sum if the series converges?

Based on the following definition:

I would need to know how I could define a and r

-

$r$th term $=\frac1{(r+1)(r+2)}=\frac{(r+2)-(r+1)}{(r+1)(r+2)}=\frac1{r+1}-\frac1{r+2}$