# Expansion is tedious

Algebra Level 4

$\large \left( 1 + \dfrac{x}{1!} + \dfrac{x^2}{2!} + \dfrac{x^3}{3!} + \ldots + \dfrac{x^n}{n!} \right )^2$

For $$n\geq 6$$, if the coefficient of $$x^6$$ in the expansion above can be expressed as $$\dfrac{a}{b}$$ for coprime natural numbers $$a,b$$, find $$\sqrt{a+b}$$.

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