(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine whether the series converges or diverges.

[tex]\sum_{n=2}^{\infty}\frac{1}{(\ln n)^{\ln (\ln n)}}=\sum_{n=2}^{\infty}\frac{1}{e^{\ln (\ln n)\ln (\ln n)}}[/tex]

3. The attempt at a solution

for [tex]u=\ln (\ln n)[/tex]

[tex]\sum_{u=\ln (\ln 3)}^{\infty}\frac{1}{e^{u^2}}[/tex]

from Root Test

[tex]\lim_{u\rightarrow\infty}\sqrt{\frac{1}{e^{u^2}}}=\lim_{u\rightarrow\infty}\frac{1}{e^u}=0<1[/tex]

series converges

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# Homework Help: Series 5.

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