ABSTRACT
This chapter clarifies what we mean by infinite series and shows that some of them behave rather unexpectedly. It helps the reader to recognize an infinite series and determine the sum to n terms of standard series. It also assists the reader in examining for convergence directly by using the sum to n terms and determining the radius of convergence of a power series. The chapter demonstrates solving of practical problems concerning radioactive emission and a leaning tower. There are very many tests which have been devised to examine infinite series to determine whether or not they converge or diverge. It is reasonable to ask whether there is one test which will settle the matter once and for all. However, there is no supertest; whatever test we have there is always a series which can be produced on which the test will fail.
