What does $ \sum_{i = 1}^{\infty} \frac{1}{i(i-1)!}$ converge to?

Question

What does $ \sum_{i = 1}^{\infty} \frac{1}{i(i-1)!}$ converge to?

That is $1 + \frac{1}{2} + \frac{1}{3*2!} + ... + \frac{1}{n(n-1)!}$

Answer 1

Hints:

For any $x\in (-\infty,+\infty)$, $$e^x=1+x+\frac{x^2}{2!}+\dots+\frac{x^n}{n!}+\dots.$$

So you can consider $e^1=?$