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Math Help - Another summation problem_

  1. #1
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    Another summation problem_

    If we have q= Σ exp(2*pi*j*k*n/N) , for n=0 to M -1

    I want to prove a condition for M such as q=0 . .

    I'm a bit confused. I start to solve it by knowing that

    Σ exp(2*pi*j*k*n/N) , for n=0 to N-1 , = 1- exp(2pi*j*k)/ 1-exp(2pi*j*k/N)

    ...

    thanks in advance

    Nikolas
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  2. #2
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    Quote Originally Posted by tsebamm View Post
    If we have q= Σ exp(2*pi*j*k*n/N) , for n=0 to M -1

    I want to prove a condition for M such as q=0 . .

    I'm a bit confused. I start to solve it by knowing that

    Σ exp(2*pi*j*k*n/N) , for n=0 to N-1 , = 1- exp(2pi*j*k)/ 1-exp(2pi*j*k/N)

    ...

    thanks in advance

    Nikolas
    Sometimes you write N, sometimes M...a mess. Anyway, you already have it!:

    \displaystyle{\frac{1-e^{2\pi jk}}{1-e^{2\pi jk/N}}=0 , of course assuming j,k\in\mathbb{Z}\,,\,jk\neq 0\!\!\pmod N , so M=N does the trick.

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Sometimes you write N, sometimes M...a mess. Anyway, you already have it!:

    \displaystyle{\frac{1-e^{2\pi jk}}{1-e^{2\pi jk/N}}=0 , of course assuming j,k\in\mathbb{Z}\,,\,jk\neq 0\!\!\pmod N , so M=N does the trick.

    Tonio
    Thanks for that. But I do not think that I understand it. When M=N then q=0 ?? What's the proof of that?
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