Evaluating a sum (begginer) I am stuck on this evalutaion number.
So the sum is $$\sum_{k=1}^n{1\over (k+1)^2}-{1\over k^2}$$
I can't find a way :(. Do we use Comparasion or partial sums?
Thanks for the help! 

$$\sum_{k=1}^n\ \left(\frac{1}{(k+1)^2} - \frac{1}{k^2}\right)$$
$S_1 = \frac{1}{2^2} - \frac{1}{1^2}$
$S_2 =\left(\frac{1}{2^2} - \frac{1}{1^2}\right)+\left(\frac{1}{3^2}-\frac{1}{2^2}\right)$
$S_3 = \left(\frac{1}{2^2} - \frac{1}{1^2}\right)+\left(\frac{1}{3^2}-\frac{1}{2^2}\right)+\left(\frac{1}{4^2}-\frac{1}{3^2}\right)$
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$S_n = -1+\frac{1}{(n+1)^2} = \sum_{k=1}^n\ \left(\frac{1}{(k+1)^2} - \frac{1}{k^2}\right)$
$\\$
From here you should be able to see what the sum goes to as $n \to \infty$.
