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Please help me out to find the limit of this series $$\lim_{n\to \infty} \sum_{i=0}^n e^{-n} \frac{n^i}{i!} $$

Upper Limit is easy to find , how to find exact limit

jimjim
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    It's not really a series, because when you go from $n$ to $n + 1$, all the terms that came before change. – user49640 Jun 12 '17 at 13:02
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    Let's start with you including your work on the problem. – amWhy Jun 12 '17 at 13:03
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    @amWhy I would prefer it if we were a bit more polite towards people posting questions. – user49640 Jun 12 '17 at 13:04
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    @user49640 My comment is not any less polite than your original comment. So there is nothing that I said that can be construed as "unpolite". – amWhy Jun 12 '17 at 13:06

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