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Homework Help: Integral for Multiple Natural Logs

  1. Jan 19, 2012 #1
    1. The problem statement, all variables and given/known data

    I need to find whether or not the Ʃ1/(n(ln n)(ln(ln(n)))) (from 2 to infinity) converges or diverges using the Integral test. I think the best question to ask is where to start with the integral?

    2. Relevant equations


    3. The attempt at a solution

    I've tried integrating by parts, but I can't find du or v for 1/(lnx)ln(ln(x)). Is there a way to simplify this into a more friendly form?
  2. jcsd
  3. Jan 19, 2012 #2


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    Science Advisor

    If you let u= ln(ln(x)) then [itex]du= (1/ln(x))(1/x)dx[/itex].
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