# Error terms in Taylor Series

by Nurdan
Tags: error, series, taylor, terms
 P: 4 It is known that $$\sum\limits_{k = 0}^\infty {\frac{{N^k }}{{k!}}} = e^N$$ I am looking for any asymptotic approximation which gives $$\sum\limits_{k = 0}^M {\frac{{N^k }}{{k!}}} = ?$$ where $$M\leq N$$ an integer. This is not an homework
 P: 530 I'm only being a little facetious if I point out that the sum is asymptotically equal to e^N. Want more accuracy? It's better approximated by e^N-[x^(N+1)]/(N+1)!

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