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Math Help - determine if series is absolutely convergent conditionally convergent or divergent

  1. #1
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    determine if series is absolutely convergent conditionally convergent or divergent

    determine if series is absolutely convergent conditionally convergent or divergent

    for sum from 1 to infinity of ((-1)^n)(n/(5+n))

    my work: absolute value of lan+1/(an)l = (n+1/(5+(n+1))(5+n/(n)) as n goes to infinity equals 5/6 which is less than 1 so the series is absolutely convergent by ratio test.

    is this right?
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  2. #2
    MHF Contributor chisigma's Avatar
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    ... unfortunately that isn't right!...

    In order to establish if the series...

    \sum_{n=1}^{\infty}(-1)^{n}\cdot \frac{n}{5+n}

    ... converges you have invoked the ratio test. In your enthusiasm however you forgot to do a preliminary test which is necessary condition for convergence. What a test is that?...

    Kind regards

    \chi \sigma
    Last edited by chisigma; April 6th 2009 at 11:00 PM.
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  3. #3
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    i still don't get where I went wrong
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  4. #4
    Senior Member Twig's Avatar
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    hi

    Hi!

    A necessary condition is that the terms go towards zero.

    What is  \lim_{n \rightarrow \infty} \, \frac{n}{5+n} ?
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