# Factorial sum

Calculus Level 5

If $$f(x)$$ is a monic $$n^{\text{th}}$$ degree polynomial such that $$f(1)=11,f(2)=32,f'''(x)=0$$ and $$\displaystyle\sum_{x=1}^{50}[(f(x))(x+1)!]=M$$ then find $\frac{M+2}{52!}$

×