Sum of all elements in congruence class modulo n With $+$ defined as $[a]+[b]=[a+b]$, show that $[0]+[1]+\cdots+[n-1]$ is equal to either $[0]$ or $[n/2]$ in $\Bbb Z_n$.
How do I go about proving this? I have managed to get $[(n^2-n)/2]$ using the definition but how do I proceed from here to the result? 
Help would be much appreciated, thanks in advance!

Without words:
$$\begin{align}&1+2+3\\
&7+6+5\end{align}\color{green}{+4}=8+8+8\color{green}{+4}$$
$$\begin{align}&1+2+3+4\\
&8+7+6+5\end{align}=9+9+9+9$$
