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Math Help - Sum of a simple series

  1. #1
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    Sum of a simple series

    Hi everybody! Problem: I don't know how to find an explicit form for this sum, anyone can help me?

    \sum_{k=-\infty}^{+\infty}\frac{1}{|x-kx_0|}

    here the calculations I made, but don't bring me anywhere:

    https://dl.dropbox.com/u/8281720/SAM_1625.JPG

    and my prof's version (I'm not sure he could be so quick on the absolute value)

    https://dl.dropbox.com/u/8281720/photo.JPG

    Thanks!
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  2. #2
    mfb
    mfb is offline
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    Re: Sum of a simple series

    The sum is invariant under a transformation x -> x+n*x0 with integer n, therefore you can assume 0 < x < x0 (not equal, as the sum would not be well-defined then).

    However, I do not see how this sum can converge at all - it is like two sums over (positive) 1/n, which have a logarithmic divergence.
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