De Moivre's Theorem and Power Series

  • Thread starter machofan
  • Start date
  • #1
machofan
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Homework Statement


Hi I'm stuck with the following question:

Use de Moivre's Theorem and your knowledge of power series to show:

1/1(1/2^1)cos(θ)+1/2(1/2^2)cos(2θ)+1/3(1/2^3)cos(3θ)+ ... = log(2)-1/2*log(5-4cos(θ))


Homework Equations




The Attempt at a Solution


I have already established the series to be (1/2)(∑((eiθ/2)^n/n) + ∑((e-iθ/2)n)/n) and evaluated the two series as a function of a natural logarithm ∑(x^n/n). But I'm not sure where to go from here, any help is much appreciated thanks.
 

Answers and Replies

  • #2
MostlyHarmless
345
15
If you're stuck, try working it from the other direction. Start with ##log(2)- (1/2)log(5-4cos\theta)##.
 

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