(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that Wn = 3^{-n}cos 2nӨ for n = 1, 2, 3, …, use de Moivre’s theorem to show that

1 + W_{1}+ W_{2}+ W_{3}+ … + W_{N-1}= [ 9 – 3 cos2Ө+ 3^{-N+1}cos2(N-1)Ө - 3^{-N+2}cos2NӨ] / [10 – 6cos2Ө]

Hence show that the infinite series

1 + W_{1}+ W_{2}+ W_{3}+ …

is convergent for all values of Ө, and find the sum to infinity

Please i need help on how to solve this above question. though I have posted it before in my blog but was deleted. I don't know the reason for the deletion. I guessed I should have posted it in homework section

2. Relevant equations

3. The attempt at a solution

I don't have a clue to this question, I have tried to use A.P and G.P formulas but proved difficult. I need help in order to teach my students preparing for external exams in further maths.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Sum of complex series

**Physics Forums | Science Articles, Homework Help, Discussion**