sequences and series - How do you prove $sum_{n=0}^infty frac{(-1)^n}{n!} = frac{1}{e}$?

prove the sum

$$\sum_{n=0}^\infty \frac{(-1)^n}{n!} = \frac{1}{e}$$

In one of the solutions to a problem I was looking at had this sum and directly got $1/e$ from it. I don't understand how you get that, I used my calculator and it indeed does equal $1/e$ but I'm interested in how you solve this by hand.