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I am having trouble determining convergence/ divergence of the following series:

$\sum\limits_{n=2}^{\infty} \frac{1}{(\log(n))^{1/n}}$

When I apply the root and ratio tests, I find in both cases the limit 1 (which means that the test is inconclusive).

Please help

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    Hint: What is $\lim\limits_{n\rightarrow\infty} \bigl(\log (n)\bigr)^{1/n}$?2012-12-12

2 Answers 2