cmf for Geometric distribution

Hi,

For the cmf of a Geometric distribution, it could be written as
sum form i=1 to t of p(1-p)^(i-1) where p is the probability of
success
or equivalently
1-(1-p)^t

I'm having some trouble in understanding how the first definition
could relate to the second definition. The books I've read doesn't
show the proof.

.