
#1
Nov411, 12:42 AM

P: 6

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 Ptest 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! 



#2
Nov411, 01:49 AM

P: 48





#3
Nov411, 03:15 AM

P: 6

n^(u/n)/u 



#4
Nov411, 04:24 AM

P: 48

Convergence of Series 


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