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Homework Help: For which values of p does this sum converge?

  1. Mar 4, 2012 #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]

    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. jcsd
  3. Mar 5, 2012 #2
    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
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