# 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