Proving sum of infinite series My statistics textbook states that $\sum\limits_{n=0}^{\infty} \begin{pmatrix}2n \\ n \end{pmatrix}(pqs^2)^n=\frac{1}{\sqrt{1-4pqs^2}}$ 
where $|s|<1$, $p \in ]0,1[$ and $q=1-p$.
That thing is that prof of this is omitted since its "not relevant". How would one prove it? 
Soo far i have never calculated a sum involving a binomial coefficient. 

Using Binomial series, for $|x|<1$ the $r(r\ge0)$th term of $$(1-x)^{-1/2}$$ is
$$\dfrac{-1/2(-1/2-1)\cdots\{-1/2-(r-1)\}}{r!}(-x)^r=\dfrac{1\cdot3\cdot5\cdots(2r-1)x^r}{r!2^r}=\binom{2r}r(x/4)^r$$
