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Convergence of a series

dwsmith

Well-known member
Feb 1, 2012
1,673
$\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$

I am trying to show that this series diverges or converges
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,725
$\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$

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 $\ln(\ln n)>2$.