An algebra problem by Saurav Pal

Algebra Level 3

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

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.

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