Which values for $a$ will make series convergent or divergent?
$ \sum_{k=1}^{\infty}\frac{1}{(2k+1)\ln^a(2k+1)} $
I have been following this tutorial http://tutorial.math.lamar.edu/Classes/CalcII/SeriesIntro.aspx But now I'm stuck. I haven't seen examples as this one above. There is additional parameter $a$ which values I have to find myself. Could anyone suggest me how should I work this time then? Maybe I just choose randomly some values for $a$? Like $a=-2$, $0$ and $2$?