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Sum of the e's

  • Thread starter happyg1
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  • #1
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Homework Statement


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:
[tex]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}[/tex]
HOW did he get that?


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

Homework Equations





The Attempt at a Solution

 
Last edited:

Answers and Replies

  • #2
Curious3141
Homework Helper
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Hint : geometric progression.

The exponents on the Right Hand Side should be 2pi, not 12 pi.
 
  • #3
682
1
[tex]x^n-1=(x-1)(1+x+x^2+x^3+x^4+x^5+...x^{n-1})[/tex]

for n=natural number.
 
  • #4
308
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Thanks. I see it now.
CC
 

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