# But how?

Calculus Level 5

$\large \displaystyle\sum_{n=1}^\infty\sum_{k=1}^\infty\sum _{ i=1 }^{ \infty }{ \dfrac { nki }{ (n+k+i)! } } =\dfrac { A }{ B } e$

The equation above holds true for coprime positive integers $$A$$ and $$B$$. Find $$A+B$$.

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

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