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 \( \displaystyle \lim_{x\to\infty} \frac{(x+1)!}{f(x)} \).

SELF MADE!

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