Convergence/divergence of series $\sum\limits_n\frac1{(\log(1+n))^p}$ $$\sum u_n\qquad u_n = \frac{1}{(\log(1+ n))^p}$$
Wolfram says it's convergent, my book proves it divergent, someone said it depends on p. Can anyone help with the actual answer?

It is obviously divergent: $(\log(n))^p<n$, for any $p>0$ and great enough $n$. On the other hand, if $p\leq 0$, the general term increases, thus the series diverges.
