Trying to solve this sum, wich involves binomial coefficient. But it looks very difficult:

$\displaystyle \sum_{n=1}^{M-1}\left(\begin{array}{cc}M\\n\end{array}\right)$$\displaystyle \sqrt{\frac{M-n}{n}}$

It is the same as:

$\displaystyle \sum_{n=1}^{M-1}\left(\begin{array}{cc}M\\n\end{array}\right)$$\displaystyle \sqrt{\frac{n}{M-n}}$

Thanks