I have gotten the first half of this question, but need help on the second half.

Let be a random variable with geometric distribution of parameter .

a)Show that satisfies the memoryless property:

Here is my answer to this half:

If has the probability distribution function ,

Then ,

Consider the following, where is some positive integer such that

Therefore,

(obtained from this source: memoryless property of geometric distribution)

b)Reciprocally, show that any random variable , having nonnegative integer values, whose distribution satisfies the property above has necessarily a geometric distribution.

I presently don't have an answer to this half of the question, so I could use a hand.