If

Then

.

This means by DeMoivre's Theorem, the focus root is

.

But there must be exactly roots, all spaced evenly about a circle.

So that means any can be written as

, where is a positive integer no greater than .

That means

But any integer multiple of gives the same result as .

So that means .

Now let's go back to the original problem...

We have .

This is a geometric series with and .

So the sum is

.

But .

So that means the sum is

.

Q.E.D.