Sum equal to Kronecker delta - how?

• November 7th 2011, 11:26 AM
kornellster
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!
• November 7th 2011, 02:33 PM
emakarov
Re: Sum equal to Kronecker delta - how?
This is a geometric progression, so use the formula $1+a+\dots+a^{N-1}=\frac{a^N-1}{a-1}$.