Find the sum of the series $\sum_{n=1}^{\infty}(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n})$ I need to test the convergence and find the sum of the following series:
$\sum_{n=1}^{\infty}(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n})$
But i am not really sure what kind of series is this?
Since 
$2\sqrt{n+1}>\sqrt{n}+\sqrt{n+2} \forall n \in \mathbb{N}$
It means that this is the series with all negative terms, what can i do with that kind of series? Can i use the same tests as for series with all positive terms (non-negative to be precise)? If that is true, then how can i use them?

Just write
$$\sqrt{n+2}-2\sqrt {n+1}+\sqrt n=(\sqrt{n+2}-\sqrt {n+1})+(\sqrt n-\sqrt{n+1})$$
and then telescope.
