I've been working through exercises in Chapter 8 of Apostol's Mathematical Analysis. Exercise 8.15 gives a number series to be tested for convergence. I've gotten most of them but I'm stuck on
$$\sum_{n=1}^\infty{1\over(\log n)^{\log n}}.$$
The root test is in conclusive, and the things I can think of to compare with have the wrong inequality. I thought I had proven divergence by the integral test, but something was wrong because according to Wolfram Alpha, this converges. Hint, anyone?
P.S. Looking to avoid Cauchy condensation test.