# Moving exclamation marks

Calculus Level 3

$\large \lim_{n \to \infty} \dfrac{n!}{!n}$

The limit above has a closed form. Find this closed form.



Notations:

• $$!$$ denotes the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

• $$!n$$ denotes the number of derangements for $$n$$ different objects, $$\displaystyle !n = n! \sum_{r=0}^n \dfrac{(-1)^r}{r!}$$.

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