In my probability class we saw an amazing proof using the CLT (central limit theorem), I'm wondering what's a more straightforward way to do this.
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How is the equation related to your question ? – callculus42 Jul 07 '16 at 05:29
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@callculus I'm asking how to prove it with standard methods. – Jul 07 '16 at 05:33
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The CLT or the equation ? – callculus42 Jul 07 '16 at 05:34
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@callculus the equation. – Jul 07 '16 at 05:34
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If you mean $\lim_{ n \to \infty} \sum_{k=0}^n \frac{n^k}{k!}\cdot e^{-n}$, then have a look here: http://math.stackexchange.com/questions/160248/evaluating-lim-limits-n-to-infty-e-n-sum-limits-k-0n-fracnkk – callculus42 Jul 07 '16 at 06:05
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@callculus Thanks! – Jul 07 '16 at 06:34