- #1

eschiesser

- 18

- 0

## Homework Statement

I am asked to find a "compact expression" for the infinite sum:

S(x) = 1 + e^(ix) + e^(2ix) + e^(3ix) +...+ e^(i*n*x)

I am given a hint: "Note that it isn't true that S(x)-1= S(x)*e^(ix), but almost. Use this fact."

## Homework Equations

e^(ix)=cos(x) + isin(x), the famous Euler's formula, is all I can think of that would be helpful in solving this.

## The Attempt at a Solution

Thus far, the only thing I have managed to do is convert the series into trigonometric terms:

1+(cosx+isinx)+(cos2x+isin2x)+... etc. I have a feeling this is not going to get me the solution though. Any insight would be appreciated. Thanks!