(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For which p > 0 does the sum

[itex]\displaystyle\sum\limits_{k=10}^∞ \frac{1}{k^p(ln(ln(k)))^p}[/itex]

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.

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# For which values of p does this sum converge?

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