Nov 28, 2012 Thread starter #1 D 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

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

Nov 29, 2012 Moderator #2 Opalg MHB Oldtimer Staff member Feb 7, 2012 2,702 dwsmith said: $\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$ I am trying to show that this series diverges or converges Click to expand... Hint: $\displaystyle\frac{1}{(\ln n)^{\ln n}} = \frac{1}{e^{\ln n \ln(\ln n)}}$, and if $n$ is large enough then $\ln(\ln n)>2$.

dwsmith said: $\sum\limits_{n = 2}^{\infty}\frac{1}{(\ln n)^{\ln n}}$ I am trying to show that this series diverges or converges Click to expand... Hint: $\displaystyle\frac{1}{(\ln n)^{\ln n}} = \frac{1}{e^{\ln n \ln(\ln n)}}$, and if $n$ is large enough then $\ln(\ln n)>2$.