oskar-
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Hi all, perhaps someone can shed some light on the following sum:
[tex] \lim_{m\rightarrow\infty}\frac{1}{m}\sum_{k=1}^{m-1}\left[1-\left(\frac{k}{2m-k}\right)^{1/2} \right]^2[/tex]
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 :)
[tex] \lim_{m\rightarrow\infty}\frac{1}{m}\sum_{k=1}^{m-1}\left[1-\left(\frac{k}{2m-k}\right)^{1/2} \right]^2[/tex]
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 :)