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...