ABSTRACT
This chapter aims to develop precise the ideas underlying the convergence of series. It examines the way in which functions may be represented in terms of series, after which it shows some of the most important ways in which series are used. Functions arising in mathematics are often defined in terms of Maclaurin or Taylor series. The chapter explores the conditions under which the power series converge to a finite number for any given value of their argument, and the error made when such a series is truncated, are developed from the tests for convergence. The applications of series are numerous and varied, and included are the use of series to evaluate indeterminate forms, the location and identification of extrema of functions of one and several real variables, the analysis of constrained extrema , and the least-squares fitting of data.
