Calculate $1+2\epsilon+3\epsilon^{2}+\cdots+n\epsilon^{n-1}$ Where $\epsilon$ is nth root of unity. There is a hint that says: multiply by $(1-\epsilon)$
Doing this multiplication I get: $1+\epsilon+\epsilon^{2}+\epsilon^{3}+\cdots+\epsilon^{n-1}-n$ The answer is: $-\frac{n}{1-\epsilon} $if $ \epsilon\neq1$ and $\frac{n(n+1)}{2}$ if $\epsilon=1$. I can't see how to get this result...