An algebra problem by Saurav Pal

$\frac{1}{2}+\frac{1\times3}{2\times4}{ \left( \frac {1}{4} \right )}+\frac{1\times3\times5}{2\times4\times6}{ \left( \frac {1}{4} \right)^{2}}+ \ldots$

If the value of the series above equals to $\frac{a}{b}(c\sqrt{d}-e)$ , what is the value of $a+b+c+d+e$ ?

Note that $a,b,c,d$ and $e$ are positive integers with $d$ is square-free.