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!

It diverges. By comparison test,
\begin{align}
\frac{\sqrt{n+1} - \sqrt{n}}{\ln{n}} &= \frac{1}{\ln{n}\left(\sqrt{n+1} + \sqrt{n} \right)} \\
&> \frac{1}{n} 
\end{align}
for $n > 100$ (say), and the harmonic series diverges.
