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Asymptotic behavior of functions, asymptotic series and related topics

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Finding the asymptotic bound of a summation

Given a sufficiently large positive integer $n$, I would like to know the asymptotic bound in $n$ of the following summation: $$ \sum_{i=0}^{n}{\frac{P(n, i)}{n^i}} = \sum_{i=0}^{n}{\frac{n!}{(n-i)! \ …