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Exponential series limit

jacks

Well-known member
Apr 5, 2012
226
Evaluation of $\displaystyle \lim_{n\rightarrow \infty}e^{-n}\sum^{n}_{k=0}\frac{n^k}{k!}$
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
Suppose the "n" in [tex]\frac{n^k}{k!}[/tex] were "x". Do you recognize [tex]\sum_{k= 0}^n \frac{x^k}{k!}[/tex] as a partial sum for the power series [tex]\sum_{k=0}^\infty \frac{x^k}{k!}= e^x[/tex]?
 
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Satya

New member
Sep 13, 2019
11
Suppose the "n" in [tex]\frac{n^k}{k!}[/tex] were "x". Do you recognize [tex]\sum_{k= 0}^n \frac{x^k}{k!}[/tex] as a partial sum for the power series [tex]\sum_{k=0}^\infty \frac{x^k}{k!}= e^x[/tex]?
So, the limit should be just 1, right?
 
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Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,714
The problem was posted in the challenge forum. Please provide full solutions. And please hide them including any hints between spoiler tags.