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Error terms in Taylor Series

by Nurdan
Tags: error, series, taylor, terms
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Nurdan
#1
Dec16-08, 02:43 PM
P: 4
It is known that
[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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christianjb
#2
Dec16-08, 09:18 PM
P: 529
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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