# Infinite Factorial Summation with Sum of Squares

Calculus Level 4

$\large \dfrac{1}{2!} + \dfrac{1^2 + 2^2}{3!} + \dfrac{1^2 + 2^2 + 3^2}{4!} + \ldots$

If the above series can be expressed as $$S$$, then find the value of $$\big \lfloor 100S \rfloor$$ .

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