In this lesson, we learn about alternating series and absolute convergence. An alternating series is a series whose terms alternate in sign, and we can determine if it converges using the convergence theorem for alternating series. We can also estimate the remainder of a convergent alternating series using certain conditions. We explore the concepts of absolute and conditional convergence and see how they relate to alternating p series and geometric series. Finally, we learn about the ratio and root tests, which allow us to determine if the sum of a sub k converges absolutely or diverges.
Convergence theorem for alternating series. Estimation of the remainder. Absolute versus conditional convergence.
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.