Does the following sequence converge, if so find the limit, if not prove that no limit exists: $a_n=(-1)^nn^2$ $$a_n=(-1)^nn^2$$
I know that this sequence does not converge and hence does not have a limit. I have tried proving that this sequence does not have a limit by contradiction. 
I assumed that the limit 'a' existed and then performed the reverse triangle inequality. Thus:
$$|(-1)^nn^2-a|<\epsilon$$
$$=|(-1)^nn^2|-|a|<\epsilon$$
From here I am stuck, I have been told that I should be considering two cases for the even and odd I believe, but am not too sure how to go forward and make these contradictions.

Hint: Recall that $(-1)^n$ does not converge and product of two convergent sequences is again convergent.
