calculus - Please give hint to find the sum of this series: $sum_{n=1}^{infty}frac{(-1)^{n-1}}{n!}$

can anyone give me some hint how to find this series's sum?

$$\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n!}$$
I know that by the ratio test, I can find that it is convergent.

But in order to find its sum, I may need some analysis technique which I don't have. thanks.

Answer

One may recall that

$$\sum_{n=0}^{\infty}\frac{z^{n}}{n!}=e^z,\quad z \in \mathbb{C}.$$