Overview:

One ancient mathematical puzzle is sometimes called the Racecourse Paradox.
A person is running a 1-mile racecourse. Of course, the runner must complete half the course (1/2 mile) before completing the entire course. But when the first half of the course is completed, the runner must complete half of what remains (1/4 mile) before finishing, and then complete half of what remains after that (1/8 mile) before finishing, and so on. Because there are infinitely many distances that the runner must complete before finishing the race, how can the runner ever hope to complete the entire course?

Our everyday experience convinces you that the runner will certainly complete the race, yet adding up infinitely many positive distances would reasonably seem to sum up to an infinite total, or at least would take forever to actually compute!

Materials:

• TI-84 Plus / TI-83 Plus

Activity:

Exploring Infinite Series