# Pointers for solving a sum

1. Aug 31, 2010

### oskar-

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. Aug 31, 2010

### Hurkyl

Staff Emeritus
That looks like a Riemann sum.