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Proving a discrete sum

  1. Dec 29, 2011 #1
    Hi,

    I need help in proving the equation in the attachment.

    Thanks
    darkfeffy
     

    Attached Files:

  2. jcsd
  3. Dec 29, 2011 #2

    Dick

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    Start by using a double angle formula to express sin(x)^2 in terms of cos(2x). Now get started.
     
  4. Dec 29, 2011 #3
    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.
     

    Attached Files:

  5. Dec 29, 2011 #4
    Thinking it might just be an assumption that this last term is exceedingly small compared to the first.
     
  6. Dec 29, 2011 #5

    Dick

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    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
  7. Dec 29, 2011 #6

    D H

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    You are correct in that the term is exceedingly small (zero is an exceedingly small number). You are incorrect in that is an assumption.
     
  8. Dec 29, 2011 #7
    Thanks Dick.
     
  9. Dec 29, 2011 #8
    Thanks DH for your brilliant reply which really doesn't add much information :-)
     
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