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

"Determine whether the following series converge:

[itex]\sum_{n \geq 2} \frac{n^{ln (n)}}{ln(n)^{n}}[/itex]

and

[itex]\sum_{n \geq 2} \frac{1}{(ln(n))^{ln(n)}}[/itex]

2. Relevant equations

The convergence/divergence tests (EXCEPT INTEGRAL TEST):

Ratio

Dyadic

Comparison

P-test

Cauchy Criterion

Root Criterion

Alternating Series Test/Leibniz Criterion

Abel's Criterion

3. The attempt at a solution

My TA said it was helpful to use the Dyadic Criterion to solve series involving logs... I believe this is an exception. It made the equation really convoluted:

[itex]\sum_{n \geq 2} \frac{2^{2k}*k*ln(2)}{(k*ln(2))^{2^{k}}}[/itex]

I'm sure I have to use some combination of the tests, but I kind of need to be pointed in the right direction... I have no idea how to work with that series..

Thank you!

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# Convergence of Series

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