Snake Oil

Calculus Level 3

f(n)=r=0n(1)nr(nr)rn \large f(n) = \sum_{r=0}^{n} (-1)^{n-r} \dbinom{n}{r} r^n

Find the closed form of limnf(n)n!\displaystyle \lim_{n \to \infty} \dfrac{f(n)}{n!}.

Give your answer to 2 decimal places.

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