# For which values of p does this sum converge?

by Jacob_
Tags: converge, values
 P: 1 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.
 Quote by 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.