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For which values of p does this sum converge? 
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#1
Mar412, 11:09 PM

P: 1

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 pseries, 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
Mar512, 01:30 PM

P: 312




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