Classroom note: On the telescoping sum

Abstract

The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apéry-like formulas, and finally ending with a class of problems that are solved by computer.

Acknowledgement

The author thanks the editor and the referees for their helpful comments.