I am having difficulty finding if this series converges or diverges:

$$\sum\_{n=0}^{\infty}\frac{(-2)^{n+1}}{n^{n-1}}$$

I am unsure of which test to use. At first, I thought I should use alternating series test, but I am unable to manipulate the numerator to $(-1)^{n+1}$. I thought I may be able to use root test, but I have no clue how to manipulate the series to do that.

What series test would I use, and how?