Convergence of Series with Logarithmic Terms

[Dustinsfl]

$\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$

I am trying to show that this series diverges or converges

 

[Opalg]

$\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$

I am trying to show that this series diverges or converges

Hint: $\displaystyle\frac{1}{(\ln n)^{\ln n}} = \frac{1}{e^{\ln n \ln(\ln n)}}$, and if $n$ is large enough then $\ln(\ln n)>2$.