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Convergence of a Series

  1. Dec 16, 2006 #1
    1. The problem statement, all variables and given/known data

    For this problem, I need to determine whether a series with the general term ln(x)/x^1.0001 will converge from x=1 to x=infinity.

    2. Relevant equations

    I'm not quite sure what the relevant equations would be for this, but I'm supposed to use one of the series convergence tests, like the ratio test, root test, integral test, comparison test, or limit comparison test.

    3. The attempt at a solution

    It seems like the integral test should apply to this problem, but for some reason I can't find the integral.
  2. jcsd
  3. Dec 16, 2006 #2


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    Dearly Missed

    Well, you know that the series will diverge or converge with the associated integral, right?
    Also remember that the logarithm of x grows slower to infinity than ANY positive power of x does.
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