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.
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