Prove by induction $ 1 + 3 + 5 ... + (2n - 1) = n^2, \forall n\in \Bbb Z $
(This is the exact question taken from my Discrete Math class final exam, i don't misread anything)
I could prove it if it was $ \forall n \in \Bbb N^\ast $, however. But it was $\forall n\in \Bbb Z$. So what happen if $n\le0$. Could anyone clarify it for me? Thanks in advance for any help you are able to provide.