# For what values of p does this series converge?

1. Dec 15, 2009

### applegatecz

1. The problem statement, all variables and given/known data
Find all values of p for which the given series converges absolutely: $$\sum$$ from k=2 to infinity of [1/((logk)^p)].

2. Relevant equations

3. 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.

2. Dec 15, 2009

### Dick

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

3. Dec 15, 2009

### oinkbanana

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

4. Dec 15, 2009

### Staff: Mentor

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