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\[\sum\limits_{k = 0}^\infty {\frac{{N^k }}

{{k!}}} = e^N

\]

My question is

\[\sum\limits_{k = 0}^M {\frac{{N^k }}

{{k!}}} = ?

\]

where $M\leq N$ an integer.

This is not an homework

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# Partial exponential sum

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