Show root of unity summation

Question

I have this math problem

Let $w$ be a root of unity with $o(w)=n$, with $n > 1$. Show that $$1 + w + w^2 + \cdots + w^{n-1} = 0$$

I'm not entirely sure how to start this problem. Would I need to use proof by induction? If so, how would I start it? Thanks.

Answer 1

Hint:

$$(1-w)(1 + w + w^2 + \cdots + w^{n-1})=1-w^n$$

and $w\neq 1$ is a root of $1$.