# A sum to the power of $$e$$

Calculus Level pending

If

$S = {\sum_{n=1}^{\infty}\frac{1}{2n}\left ( \sum_{k=0}^{\infty}\frac{1}{2^{k}k!} \right )^{n}}$

Suppose $$e^{S}$$ may be written as

$\frac{a}{b-\sqrt{c \times e}}$

Then find $$a + b + c$$.

OBS:

• $$e$$ is the base of the natural logarithm.
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