Use complex exponentials to prove 1 + acos(theta) + a^2cos(2theta) + a^3cos(3theta)... = (1 - acos(theta))/(1 - 2acos(theta) + a^2)
euler's e^itheta/2 +e^-itheta/2=2cos(2theta)
The Attempt at a Solution
a^(n)cos(ntheta) = e^nitheta = e^-nitheta
from there i got the series
now from here I think I setup the summation formula but this is where I get stuck. Any help is greatly apprecited.