Calc 2 - Sequence convergence (ratio/root test?)

Test the following for absolute convergence, divergence, and convergence:

(n/(ln(n)^n ))

This one is nasty for me. I tried both the ratio and root test, and seemed to only get ugly limits of ratios/roots. Typically these problems are pretty clean, so I assume I'm doing something wrong. Additionally, Wolfram Alpha is telling me I'm wrong, and that's definitely an indicator that I'm doing something wrong.

I went through the root test all the way, and this is what I got:

a_n = n/ ln(n) ^n

|a_n|^(1/n) = (n)^(1/n) / ln (n)

lim n-> infinity (n)^(1/n) / ln (n) =^H lim (n^n + n^n ln (n))/(1/n)

= lim (nn^n + nn^n ln (n))

which goes to infinity, meaning the series is divergent, while wolfram tells me it's convergent. What am I doing wrong?