Use complex numbers and geometric series to sum: .
I don't really have a clue what to do... any help would be appreciated... thanks. The answer is .
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The key point is to use de Moivre's formula:
And mix it with the geometrical sum http://en.wikipedia.org/wiki/De_Moivre's_formula
PS. It can also be done using telescoping sums
Just be careful what Simba posted does not work for . (Because that is the special case of geometric series which fails).
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