# Sum up all of them! (1)

Calculus Level 3

$\large A = \sum_{n=0}^\infty \dfrac{ \binom n0}{n!} + \sum_{n=1}^\infty \dfrac{ \binom n1}{n!} + \sum_{n=2}^\infty \dfrac{ \binom n2}{n!} + \cdots$

Given that $$A$$ has a closed form. Find $$\lfloor 1000A \rfloor$$.

Notation: $$\dbinom MN$$ denotes the binomial coefficient, $$\dbinom MN = \dfrac{M!}{N!(M-N)!}$$.

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