# Not ordinary sum-1

Calculus Level 4

$\large \sum _{ n=1 }^{ \infty }{ \dfrac { { n }^{ 3} }{ { 3 }^{ n }\cdot n! } } =\dfrac { c~\sqrt [ a ]{ e } ~\pi^{d-1}}{ b }$

If the equation above holds true for positive integers $$a$$, $$b$$, $$c$$, and $$d$$, while $$c$$ and $$b$$ are coprime, find $$a+b+c+d$$.

Clarification: $$e \approx 2.71828$$ denotes the Euler's number.

Also try part-2 here.

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