Introduction to Power Series and Functions

A power series is a type of series with terms involving a variable. More specifically, if the variable is [latex]x[/latex], then all the terms of the series involve powers of [latex]x[/latex]. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power series.