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Math Help - Sum equal to Kronecker delta - how?

  1. #1
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    Sum equal to Kronecker delta - how?

    I am to show that the following is true:
    \frac{1}{N}\sum_{g=0}^{N-1}exp\left( 2 \pi i (l'-l) \frac{g}{N}\right)=\delta_{l'l}
    I understand that for l=l' it's equal to 1, but how to I get zero for l \neq l' ?
    Also note that l,l',N,g are integers

    Thanks for the help!
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  2. #2
    MHF Contributor
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    Re: Sum equal to Kronecker delta - how?

    This is a geometric progression, so use the formula 1+a+\dots+a^{N-1}=\frac{a^N-1}{a-1}.
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