Let be the sample space = {0, 1, 2 . . .}, And define a distribution function

Let Ω be the sample space Ω = {0, 1, 2 . . .}, And define a distribution function by m (j) = (1 − r)j r ,
For some fixed r, 0 < r < 1, and for j = 0, 1, 2,. Show that this is a distribution function for Ω.