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Math Help - Series convergence

  1. #1
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    Series convergence

    I have two series:
     \sum_{n=13}^{\infty} (-1)^{\left\lfloor \frac{n}{13} \right\rfloor} \frac{lnn}{nln(lnn)} . I wanted to 'group' terms but I had a problem with idices.

     \sum_{n=1}^{\infty} (-1)^{n} \frac{2lnn}{(n+1)^{0,5}} I tried the Leibniz's, Dirichlet's, Abel's tests but they gave me nothing. Any hints how to cope with them?
    Last edited by Lisa91; January 15th 2013 at 12:36 PM.
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  2. #2
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    Re: Series convergence

    Hi Lisa91!

    Let's start with the second.

    You said you tried Leibniz and that it gave you nothing.
    From the formula there's a pretty good match with Leibniz's test, so let's investigate.

    Can you find \lim_{n \to \infty} {2 \ln n \over (n+1)^{0.5}}?
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  3. #3
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    Re: Series convergence

    Well, I suppose it's 0 but I'm not so sure I know how to prove it. I wanted to show that the sequence declines but I couldn't finish it.
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  4. #4
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    Re: Series convergence

    Yes, it is zero.
    So if it is also decreasing, we can apply Leibniz.

    Let's start with the first criterion.
    Are you aware of l'H˘pital's rule?
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  5. #5
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    Re: Series convergence

    The "power" of any log is 0, and the power of the denominator is 0.5, so the ratio will go to 0.
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  6. #6
    Super Member ILikeSerena's Avatar
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    Re: Series convergence

    I'm guessing that's a no?
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