Find $\displaystyle S_N$ where

$\displaystyle S_N=$$\displaystyle \sum_{n=N}^{N^2}(\frac{1}{n(n+1)}$

and determine

$\displaystyle S_N$ when

$\displaystyle \lim_{N \to infinity}$

I already got

$\displaystyle \sum_{n=N}^{N^2}\frac{1}{n(n+1)}=\frac{1}{N}-\frac{1}{N^2+1}$

using the method of differences but how do I use the limit to find its value at infinity?