# Can you generalize this!

Calculus Level 4

Let $$\displaystyle f(x) = \sum_{n=1}^\infty \left( \frac1{\displaystyle \prod_{i=1}^x (n+i)}\right)$$. Evaluate the limit $$\displaystyle \lim_{x\to\infty} \frac{(x+1)!}{f(x)}$$.