Introduction to Taylor and Maclaurin Series

In the previous two sections we discussed how to find power series representations for certain types of functions––specifically, functions related to geometric series. Here we discuss power series representations for other types of functions. In particular, we address the following questions: Which functions can be represented by power series and how do we find such representations? If we can find a power series representation for a particular function [latex]f[/latex] and the series converges on some interval, how do we prove that the series actually converges to [latex]f[/latex]?