Prove by induction $ 1 + 3 + 5 ... + (2n - 1) = n^2, \forall n\in \Bbb Z $ 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.

You should read the series as ${\displaystyle\sum_{1 \le i \le n}} (2i-1)$. When $n < 1$ it's the empty sum, $0$. So the statement is, in fact, false for $n < 0$, though true for $n=0$.
