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## Homework Statement

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

## Homework Equations

## 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.