Snake Oil

Calculus Level 3

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

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

Give your answer to 2 decimal places.

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