Series convergence test $$\sum_{n=1}^{\infty} \frac{1}{(\log{n})^{(\log n)}}$$
I tried using Cauchy's condensation test:
$$\sum_{n=1}^{\infty} 2^n\frac{1}{(\log{2^n})^{(\log 2^n)}}$$
Assume that the log is of base 2:
$$\sum_{n=1}^{\infty} 2^n\frac{1}{n^{n}}$$
$$\sum_{n=1}^{\infty} \left(\frac{2}{n}\right)^n$$
And now I'm stuck.
Thanks in Advance.

The series $\sum_{n=1}^\infty(\frac{2}{n})^n$ converges, since $(\frac{2}{n})^n\leq(\frac{1}{2})^n$ for $n\geq 4$.
