# For which values of p does this sum converge?

1. Mar 4, 2012

### Jacob_

1. The problem statement, all variables and given/known data
For which p > 0 does the sum
$\displaystyle\sum\limits_{k=10}^∞ \frac{1}{k^p(ln(ln(k)))^p}$
converge?

2. Relevant equations
1/k^p converges for p > 1.

3. The attempt at a solution
I'm not really sure where to start. I want to use a comparison test with the p-series, but ln(ln(k)) < 1 for k < e^e, so the equation isn't greater or less than 1/k^p for the entire sum interval.

2. Mar 5, 2012

### sunjin09

Convergence of the series is determined only by the asymptotic behavior of the terms in the sum, for any finite k, the term is finite, and therefore irrelevant