This article presents two new elementary derivations of the expectation of the geometric distribution. I also review six existing approaches. I hope that this article will benefit instructors and students in an introductory probability course.

Students in their first course in probability will often see the expectation formula for nonnegative continuous random variables in terms of the survival function. The traditional approach for deriving this formula (using double integrals) is well-received by students. Some students tend to...