$p \in \mathbb{R}$ so that $\mu(\{n\}):=n^p(-1)^n, n \in \mathbb{N}$ is a signed measure

Question

$(\Omega,\mathcal{A)=(\mathbb{N}, \mathcal{P}(\mathbb{N}))}$

$\mu(\{n\}):=n^p(-1)^n, n \in \mathbb{N}$

For which $p \in \mathbb{R}$ is $\mu$ a signed measure?

I know the definition of signed measure but unfortunately I'm not able to do this task.