Proving that the sequence $n^{(-1)^{n}}$ is divergent I would like to prove that the sequence $n^{(-1)^{n}}$ is divergent. 

My thoughts: I know $(-1)^n$ is divergent, so $n$ to the power of a divergent sequence is still divergent? I am not sure how to give a proper proof, pls help!
The argument that "n to the power of a divergent sequence is divergent" does not make sense (consider $n^{-n}$ for example.). Regarding your sequence: if this sequence were convergent against some limit value $a$, then every subsequence would have to converge against the same value $a$. Now look at the subsequences for $n$ even and odd, respectively.
If $n$ even then $-1^n = 1 $
$$n^1 = n\Rightarrow \lim\limits_{n \rightarrow \infty}{({n})} = \infty$$ 

If $n$ odd then $-1^n = -1 $
$$n^{-1} = \frac{1}{n}\Rightarrow \lim\limits_{n \rightarrow \infty}{(\frac{1}{n})} = 0$$