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  1. #1
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    Question series- Real Analysis

    (-1)^n  n^n/ (n+1)to the power (n+1).
    I dont know how to show if it converges or diverges?

    Any ideas?
    Last edited by hebby; February 13th 2010 at 08:20 PM.
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  2. #2
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    did you try the Leibniz test?
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  3. #3
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    I need to use the AbeL test...i think, but im not sure how to use it
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by hebby View Post
    (-1)^n  n^n/ (n+1)to the power (n+1).
    I dont know how to show if it converges or diverges?

    Any ideas?
    \frac{n^n(-1)^n}{(n+1)^{n+1}}=\frac{(-1)^n}{n+1}\cdot\left(1+\frac{1}{n}\right)^n\to 0\cdot e?
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  5. #5
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    Question

    so the series converges to 0?
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by hebby View Post
    so the series converges to 0?
    Uh...yes.
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  7. #7
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    Quote Originally Posted by Drexel28 View Post
    Uh...yes.
    will let be conditional convergence as the abs. values will make 1/n+1 divergent?
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  8. #8
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    Quote Originally Posted by hebby View Post
    will let be conditional convergence as the abs. values will make 1/n+1 divergent?
    Are we evaluating this?

    \sum_{n=1}^\infty \frac{(-1)^n}{n+1}\cdot\left(1+\frac{1}{n}\right)^n
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  9. #9
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    yes
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  10. #10
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    Quote Originally Posted by hebby View Post
    yes
    Then it converges conditionally, as you stated.
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