# why is the DFS of a delta function equal to 1

I have a x[n] = $\delta$[n]. By formula is should be

$$X[k]= \sum_{n=0}^{N-1} \delta[n]W_N^{kn} X[k]= \sum_{n=0}^{N-1} e^{-j2*pi*kn/N}$$

The formulae isn't showing for some reason. I took a screenshot of what I got here: http://imgur.com/6j0Ibgu

basically why is the summation of an exponential term going to 1. $W_N=e^{-j*2*pi*k*n/N}$ in this case. I tried to prove it via $\sum\alpha^k=\frac{1-\alpha^N}{1-\alpha}$ but it doesn't work for me.

$X[k]= \sum_{n=0}^{N-1} \delta[n]W_N^{kn} \quad$, where $\>W_N^{kn}=e^{−j\,2\pi k\,n/N}$
What is the value of $\delta[n]$ when $n \neq 0 \>$ ?