Sum equal to Kronecker delta - how?

**kornellster** · November 7th 2011, 10:26 AM

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!

**emakarov** · November 7th 2011, 01:33 PM

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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