# Sum of the e's

1. Mar 24, 2007

### happyg1

1. The problem statement, all variables and given/known data
hi,
I'm working on constructible things again and in one of the proofs our prof threw out this identity and I just don't know where it came from:
$$1+e^{\frac{2\pi}{7}i}+e^{\frac{4\pi}{7}i}+e^{\frac{6\pi}{7}i}+e^{\frac{8\pi}{7}i}+e^{\frac{10\pi}{7}i}+e^{\frac{12\pi}{7}i}=\frac{e^(\frac{12\pi}{7}i)^7-1}{e^{\frac{12\pi}{7}i}-1}$$
HOW did he get that?

Edit: I can't tell if the final term is supposed to be 2pi of 12 pi. I dunno.
2. Relevant equations

3. The attempt at a solution

Last edited: Mar 24, 2007
2. Mar 24, 2007

### Curious3141

Hint : geometric progression.

The exponents on the Right Hand Side should be 2pi, not 12 pi.

3. Mar 24, 2007

### tim_lou

$$x^n-1=(x-1)(1+x+x^2+x^3+x^4+x^5+...x^{n-1})$$

for n=natural number.

4. Mar 24, 2007

### happyg1

Thanks. I see it now.
CC