# Maybe this is not Calculus

Calculus Level 3

$\large \lim_{n \to \infty } \frac{(n!)^{2}}{\displaystyle \sum_{k=1}^{n} \left(\frac{n!}{k} \right )^{2}}$

If the value of the limit above is $$x$$, and if the expression $$\displaystyle \frac { 4\left \lfloor \pi^{2}x \right \rfloor + 1 }{7 }$$ can be expressed in the form $$\large \frac {a^{2}}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. Determine $$a + b$$.

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