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[tex] \sum\limits_{k = 0}^\infty {\frac{{N^k }}{{k!}}} = e^N[/tex]

I am looking for any asymptotic approximation which gives

[tex] \sum\limits_{k = 0}^M {\frac{{N^k }}{{k!}}} = ? [/tex]

where [tex]M\leq N[/tex] an integer.

This is not an homework

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# Error terms in Taylor Series

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