Q:

Which test for Series Convergence/Divergence?

I'm after some advice please... Given the following series :
$$ \sum_{n=2}^{\infty} \frac{(ln(n+1)+n)^a}{ln^2(n)}, a>1 $$
What would be the appropriate test to perform to find whether is it Convergent or not?  I'm thinking an Integral Test but would a Comparison Test be better?
Any pointers appreciated, thankyou.

A:

Note that we don't have the necessary condition for convergence $a_n\to 0$, indeed
$$\frac{(\ln(n+1)+n)^a}{\ln^2(n)}=n^a\frac{(\frac{\ln(n+1)}{n}+1)^a}{\ln^2(n)}\to+\infty$$

