Testing Convergence of Series: \Sigma^{\infty}_{n=1}\left[1/3^{ln\:n}}\right]

[hobbes33]

\Sigma^{\infty}_{n=1}\left[1/3^{ln\:n}}\right]

How do I go about testing the convergence of this series?

I have no clue which method I should be using, since most tests fails on this one.

You don't have to show me everything, just a nudge in the right direction should get me going on this question :)

 

[zcd]

Might help to know that 3^{\ln{n}}=3^{\frac{\log_{3}{n}}{\log_{3}{e}}}=n^\frac{1}{{\log_{3}{e}}}

 

[hobbes33]

Might help to know that 3^{\ln{n}}=3^{\frac{\log_{3}{n}}{\log_{3}{e}}}=n^\frac{1}{{\log_{3}{e}}}

Ah, here's the critical link. I got it, thanks! :D