In this lesson, we explore the concept of power series, starting with the definition of a function defined by a power series. We see how a power series can be viewed as the limit of a sequence of polynomials, and how closed forms for series can be derived from geometric series. The radius of convergence theorem is also introduced, which provides us with a way to determine the domain of a power series. Finally, we explore the differentiation and integration of power series using power rules.
Functions defined by power series. Ratio and root tests for absolute convergence. Differentiation and integration. Closed forms for series derived from geometric series. Series expansions of ln(1+x) and inverse tan (x).
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.