Homework Help: Proving a discrete sum

1. Dec 29, 2011

darkfeffy

Hi,

I need help in proving the equation in the attachment.

Thanks
darkfeffy

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• equation.png
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2. Dec 29, 2011

Dick

Start by using a double angle formula to express sin(x)^2 in terms of cos(2x). Now get started.

3. Dec 29, 2011

darkfeffy

Here is my work in the attachment. I just fail to see how the last term in the last expression (sum(cos(2pi*i/w))) is equal to 0.

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• equation2.png
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4. Dec 29, 2011

darkfeffy

Thinking it might just be an assumption that this last term is exceedingly small compared to the first.

5. Dec 29, 2011

Dick

Do you know Euler's formula, e^(ix)=cos(x)+i*sin(x) (i the imaginary unit, not the integer index)? That would let you treat the sum of the cos term as the real part of the sum of a geometric series. And no, there's no approximation here. The cos part really does sum to zero.

Last edited: Dec 29, 2011
6. Dec 29, 2011

D H

Staff Emeritus
You are correct in that the term is exceedingly small (zero is an exceedingly small number). You are incorrect in that is an assumption.

7. Dec 29, 2011

darkfeffy

Thanks Dick.

8. Dec 29, 2011

darkfeffy

Thanks DH for your brilliant reply which really doesn't add much information :-)