Find all [itex]p \geq 0[/itex] such that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum_{k=1}^{\infty} \frac{1}{k \, (\log (k+1))^p}[/tex]

converges.

It looks like the integral test is the most likely candidate, but I haven't been able to make any progress using it. I'd appreciate a push in the right direction.

Edit:

I've managed to prove that it converges for [itex]p > 1[/itex]. Since it obviously diverges for [itex]p=0[/itex], I'm trying to see what happens when [itex]0 < p \leq 1[/itex].

Edit2:

And now I just proved that it diverges for such p. Problem solved.

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# Homework Help: Infinite series

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