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Math Help - convergence / divergence of a series

  1. #1
    Senior Member Sambit's Avatar
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    Question convergence / divergence of a series

    Does the following series converge?
     \sum_{n=1}^{\infty} \frac{1}{(\log_{e} 2n)\sqrt{n}}
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    \frac{1}{\sqrt{n}ln(2n)}>\frac{1}{nln(2n)}, and now use the integral test...

    The sum is diverges.
    Last edited by Also sprach Zarathustra; October 21st 2010 at 08:02 AM. Reason: sorry
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  3. #3
    Senior Member Sambit's Avatar
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    here the first sequence  f(x) is monotonically decreasing, and its limits is 0 when   n tends to infinity. but the sequence  g(x) is a sequence of real numbers, but wikipedia says that for Dirichlet's test,  g(x) should be a sequence of complex numbers[/tex]

    what do you say?
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by Sambit View Post
    here the first sequence  f(x) is monotonically decreasing, and its limits is 0 when   n tends to infinity. but the sequence  g(x) is a sequence of real numbers, but wikipedia says that for Dirichlet's test,  g(x) should be a sequence of complex numbers[/tex]

    what do you say?
    There is Dirichlet's test for real sums also...

    I was mistaken in my first direction, hopefully my post above is "the" correct way...
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  5. #5
    Senior Member Sambit's Avatar
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    got it. thanks.
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