Fourier transform for Discrete signal

[electronic engineer]

let us asuume this discrete signal:

f(n)=a^n * u(n) ; where u(n) is unit step function
; u(n)=1 where n>=0
u(n)=0 where n<0
;0=<a<1
and the foruier transform for discrete signals is defined as :
F(i)=sum ( f(n)*e^(-j2*pi*n/N) ;n=0 to inifinity

i know that the sum is equal to:

F(i)=sum(1/(1-a*e^-j2*pi*n/N)

but actually i don't know why! could anyone help!


thanks in advance!

 

[George Jones]

Hint: think infinite geometric series. In this example, what is the common ratio r?

Regards,
George

 

[electronic engineer]

what do you mean by common ratio r?