Hi,

In a derivation for the expectation of an RV with a geometric distribution I have the following:

I have several questions.

1. What sorcery took place with the binomial coefficient and k, such that k disappeared, r appeared as a factor and its now rather than ?

2. Presumably the logic is that . Can anyone show me how to prove this and what class of distribution is this, not binomial right?

Many thanks in advance. MD.