Hi. I'm trying to understand an example in a chapter on Series and Convergence. The example states rather casually that:

The nth partial sum of the series

$\displaystyle \sum^{\infty}_{n=1}{(\frac{1}{n}-\frac{1}{n+1})} = (1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + ...$

is given by

$\displaystyle S_{n} = 1 - \frac{1}{n+1}$

But I'm not understanding how we we came to this conclusion. Can somebody help me understand this?