Question:medium

Value of $\lim_{n \rightarrow \infty} e^{-n}\left(1+n+\frac{n^{2}}{2 !}+\dots+\frac{n^{n}}{n !}\right)$ is

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This is a famous result in probability. The sum of the first $n+1$ terms of the Taylor series for $e^n$, divided by $e^n$, always tends to $0.5$ because $n$ is the mean (and nearly the median) of the $Poisson(n)$ distribution.
Updated On: Jun 6, 2026
  • $0$
  • $1$
  • $1/2$
  • $\infty$
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The Correct Option is C

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