random walk probability problem

Hi, I'm working through some math ecology stuff and I'm trying to understand how the author comes up with the following:

The author claims that this Bernouilli distribution:

$\displaystyle

p(m,n) = ({1 \over 2})^n {n! \over ((n + m)/2)! ((n - m)/2)!}

$

converges to this Gaussian distribution when n approaches infinity:

$\displaystyle

\lim_{n \to \infty} p(m,n) = (2/{\pi}n)^{1/2}exp(-m^2/2n)

$

Does anybody know why that would be? The probability is for a particle arriving at point *m* on a number line after *n* moves.

jjmclell