Convergence of $\sum \frac{1}{\ln n}(\sqrt{n+1} - \sqrt{n})$ Show that 
$$ \sum\frac{1}{\ln n}(\sqrt{n+1} - \sqrt{n})$$
Converges.
I've tried the telescopic property or even write it as
$$\sum \frac{1}{\ln n (\sqrt{n+1}+\sqrt{n})}$$
But didnt help.
Thanks in advance!

Sorry, but it diverges, sinces the general term is equivalent to $\frac{1}{n^{1/2}\ln(n)}$ (Bertrand series).
