For what values of p does this series converge?

[applegatecz]

Homework Statement

Find all values of p for which the given series converges absolutely: \sum from k=2 to infinity of [1/((logk)^p)].

Homework Equations

The Attempt at a Solution

I've tried the ratio test, the root test, limit comparison test ... everything. I know the answer is the null set (that is, for no values of p does the series converge), but I can't prove that rigorously.

 

[Dick]

Do a comparison test with 1/k. Can you show lim k->infinity (log(k))^p/k=0?

 

[oinkbanana]

have you considered simply looking at this question as a "p-test"

 

[Mark44]

have you considered simply looking at this question as a "p-test"

The series is not a p-series, so this test is not applicable. Here is a p-series:
\sum_{n = 1}^{\infty} \frac{1}{n^p}