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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.