# Infinite factorial summation

Calculus Level 4

$\large \dfrac{1}{3 !} + \dfrac{2}{5 !} + \dfrac{3}{7 !} + \dfrac{4}{9 !} + \ldots$

If the series above can be expressed as $$S$$, find the value of $$\big \lfloor 1000S \rfloor$$.

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