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For what values of p does this series converge?

  1. Dec 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Find all values of p for which the given series converges absolutely: [tex]\sum[/tex] from k=2 to infinity of [1/((logk)^p)].

    2. Relevant equations

    3. The attempt at a solution
    I've tried the ratio test, the root test, limit comparison test ... everything. I know the answer is the null set (that is, for no values of p does the series converge), but I can't prove that rigorously.
  2. jcsd
  3. Dec 15, 2009 #2


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    Science Advisor
    Homework Helper

    Do a comparison test with 1/k. Can you show lim k->infinity (log(k))^p/k=0?
  4. Dec 15, 2009 #3
    have you considered simply looking at this question as a "p-test"
  5. Dec 15, 2009 #4


    Staff: Mentor

    The series is not a p-series, so this test is not applicable. Here is a p-series:
    [tex]\sum_{n = 1}^{\infty} \frac{1}{n^p}[/tex]
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