MHB Convergence of Series with Logarithmic Terms

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

I am trying to show that this series diverges or converges
 
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dwsmith said:
$\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$

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 $\ln(\ln n)>2$.
 
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