(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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."

2. Relevant 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.

3. 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!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Infinite Sum of e^(n*i*x) terms n=0,1,2

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