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Error terms in Taylor Series 
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#1
Dec1608, 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 


#2
Dec1608, 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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