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Calculus II - Series Comparison Test Problems

  1. Aug 10, 2009 #1
    1. The problem statement, all variables and given/known data

    I have two relatively similar problems:

    1.) Sigma n=1 to infinity ((ln n)^3 / n^2)
    2.) Sigma n=1 to infinity (1 / sqrt(n) * (ln n)^4)

    I'm to prove their convergence or divergence using either the direct comparison test or the limit comparison test.

    I understand both comparison tests, however, I am very much stumped on how to determine a working bn for the problems.

    3. The attempt at a solution

    I've tried using a known p-series, such as 1/(n^2) for problem #1, which is convergent. However, that p-series is not greater than the an in this case.

    I'd appreciate any sort of direction on this.
  2. jcsd
  3. Aug 10, 2009 #2


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    ln(n) grows more slowly than any power x^p for p>0. Can you suggest an interesting value of p that's relevant for 1) or 2)?
    Last edited: Aug 10, 2009
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