
We undertake a study of an important class of infinite series.

Power series are a special and very important type of infinite series. These are series which involve a variable (usually $x$ or $t$) and are much like polynomials in the variable except that the degree of each term increases without limit. We will learn about the basic form of power series, determine when (for which values of the variable) the series is convergent, and use these series to approximate important functions (and sometimes use knowledge of special functions to evaluate the sum of the series).