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Math Help - Comparison or Limit Comparison Test Problem

  1. #1
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    Comparison or Limit Comparison Test Problem

    I need to make a suitable comparison or limit comparison to determine whether

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

    converges or diverges. I know it converges but cannot find a suitable comparison to show this with.
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  2. #2
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    Quote Originally Posted by crymorenoobs View Post
    I need to make a suitable comparison or limit comparison to determine whether
    (sum from n=2 to infinity of) (1/(ln n)^(ln n))
    converges or diverges. I know it converges but cannot find a suitable comparison to show this with.
    Hint: Can you prove that \left( {\ln (n)} \right)^{\ln (n)}  = n^{\ln \left[ {\ln (n)} \right]} ?
    Last edited by Plato; March 12th 2010 at 07:48 AM.
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  3. #3
    Member Miss's Avatar
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    @Plato: it should be n not x.
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