# Thread: Basic Summation

1. ## Basic Summation

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

and determine
$S_N$ when
$\lim_{N \to infinity}$

I already got
$\sum_{n=N}^{N^2}\frac{1}{n(n+1)}=\frac{1}{N}-\frac{1}{N^2+1}$
using the method of differences but how do I use the limit to find its value at infinity?

2. Add the two rational expressions to get quad/cubic and go from there.

3. Your answer confuses me. Which 2 rational expressions $\frac{1}{N}$ and $\frac{1}{N^2+1}$, that gives me,

$\frac{N^2+1-N}{N(N^2+1}$

which still doesen't help me.