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Homework Help: Help with showing infinite series converges/diverges

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine whether the series converges or diverges

    1/2(ln(n+1))^2 from n = 1 to infinity

    3. The attempt at a solution

    Cannot find anything to compare this series to that will show it diverges. Ratio and root test both fail. Integral test requires integrating to a non-elementary anti derivative. I have no clue how to find a solution to this.
  2. jcsd
  3. Feb 26, 2012 #2


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    Science Advisor
    Homework Helper

    You probably mean [itex]\frac{1}{2 \ln(n+1)^2}[/itex], think about comparing it with [itex]\frac{1}{n}[/itex]. Which do you think is larger for large values of n? Now can you prove it?
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