# 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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