sequences and series - Convergence of $sum_{n=2}^{infty}frac{1}{nlog(log n)^s}$

Does this series converge?
$$\sum_{n=2}^{\infty}\frac{1}{n\log(\log n)^s}$$
I wrote it as

$$\sum_{n=2}^{\infty}\frac{1}{ns\log(\log n)}$$
and I dont know how to deal with the double logarithm. This has to be shown with Cauchy's condensation test.

Answer

Use Cauchy's Condensation Text , assuming $\;s>0\;$ (otherwise divergence is almost trivial) :

$$\frac{2^n}{2^n\log(\log 2^n)^s}=\frac1{s\log(n\log2)}=\frac1{s\log n+s\log\log2}$$

and since the last term's series clearly diverges also ours does diverge.