Question:what does p need to be for this to be convergent

sum from 1 to infinity of $\displaystyle \frac{(-1)^{n-1}}{n^{p}}$

Answer: p>0

Confusion: I thought it would have to be p>1 like the "p-series" ($\displaystyle \frac{1}{n^{p}}$ is convergent for p>1)