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### Find lim$_{n \to \infty} \sum _{ k =0}^ n \frac{e^{-n}n^k}{k!}$ [duplicate]

We need to find out the limit of, lim$_{n \to \infty} \sum _{ k =0}^ n \frac{e^{-n}n^k}{k!}$ One can see that $\frac{e^{-n}n^k}{k!}$ is the cdf of Poisson distribution with parameter $n$. Please ...
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### Closed Form for $~\lim\limits_{n\to\infty}~\sqrt n\cdot(-e)^{-n}\cdot\sum\limits_{k=0}^n\frac{(-n)^k}{k!}$

$\qquad\qquad\qquad$ Does $~\displaystyle\lim_{n\to\infty}\frac{\sqrt n}{(-e)^n}\cdot\sum_{k=0}^n\frac{(-n)^k}{k!}~$ possess a closed form expression ? Inspired by this frequently asked question, I ...