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Pointers for solving a sum

  1. Aug 31, 2010 #1
    Hi all, perhaps someone can shed some light on the following sum:

    \lim_{m\rightarrow\infty}\frac{1}{m}\sum_{k=1}^{m-1}\left[1-\left(\frac{k}{2m-k}\right)^{1/2} \right]^2

    What particularly throws me off is having the m variable as part of the summands. I have ran numerical simulations and it appears to "converge" to a constant as m grows large.

    Any pointers to some theory that could help me solve this is greatly appreciated :)
  2. jcsd
  3. Aug 31, 2010 #2


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    That looks like a Riemann sum.
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