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Math Help - sum infinite serie

  1. #1
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    sum infinite serie

    somebody know how to calcualte the following series
    \sum _{m=1}^{\infty } (-1)^m(\text{Log}[m+a])
    a>0
    I think that is semi convergent
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  2. #2
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    Re: sum infinite serie

    The sum does not converge at all...

    http://www.wolframalpha.com/input/?i...+1+to+infinity
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  3. #3
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    Re: sum infinite serie

    Quote Originally Posted by capea View Post
    somebody know how to calcualte the following series
    \sum _{m=1}^{\infty } (-1)^m(\text{Log}[m+a])
    a>0
    I think that is semi convergent
    As with some other posts, what type of summation are you interested in? (not that it should make much difference)

    Since this has a relatively mild divergence one would hope that the Abel sum of this would exist, and some numerical experiments suggest that it does have an Abel sum for at least some values of a.

    Wolfram Alpha fails to find an Abel summation or a Lindelöf sum, but that does not mean that they don't exist, since your question appears to have been written in Mathematica syntax have you tried implementing your preferred summation method in that?

    CB
    Last edited by CaptainBlack; July 14th 2011 at 11:33 AM.
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  4. #4
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    Re: sum infinite serie

    one time a read a book of divergent series of Mr Hardy
    and a found a sum
    \sum _{m=1}^{\infty } (-1)^{m+1} (\text{Log}[m+1])=\frac{1}{2} \text{Log}\left[\frac{\pi }{2}\right] it is possible found it using mclauring Euler i try to extend the sum for other values.
    bur wolfram alpha only give the partial sum

    sorry for my english lenguage.
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