You declare to be a variable that takes on positive integers. is not a positive integer. So, the probability that must be 0, right? But, that implies that the probability that must be 0 for all positive integers . Did you mean is a variable that can be any nonnegative integer?

Now, .

And in general,

Plugging that in, we have

.

Now, you know , so implies .

Does that help at all?