Hi. I need help in the following problem please.

If , where is a positive integer, prove that:

Thank you

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- Mar 26th 2011, 03:27 AMmohammadfawazFinite sum question
Hi. I need help in the following problem please.

If , where is a positive integer, prove that:

Thank you - Mar 26th 2011, 04:30 AMHallsofIvy
I haven't worked out the whole thing but I think that the fact that the indices in the result are multiples of 4 would lead to looking at z= i. Recall that if z= i, then , , and [itex]z^4= 1[/tex]. That is, taking z= i gives, as real part, .

- Mar 26th 2011, 06:04 AMmohammadfawaz
Thanx...

it actually worked..

I took z = i, then -i, then 1, then -1. the complex part vanishes and I got a system of two equations two unknowns : (z0 + z4 + z8 + ...) and (z2 + z6 + z10 + ... )