Alternating Series and Absolute Convergence

Alternating Series and Absolute Convergence
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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.
Convergence theorem for alternating series. Estimation of the remainder. Absolute versus conditional convergence.
  • What is an alternating series?
  • What is absolute convergence?
  • What is the alternating harmonic series?
  • How do you know if an alternating series will converge?
  • Does the sum of (-1)^k/2k+1 converge or diverge?
  • How do you estimate the nth remainder of a converging alternating series?
  • How do you estimate the difference between the sum from k=1 to infinity of (-1)^(k-1)/k and its 100th partial sum?
  • What is conditional convergence?
  • What are alternating p-series?
  • When do geometric series converge absolutely?
  • For what values of x does the sum of x^k/k converge absolutely, converge conditionally, and diverge?
  • Why does it matter if a series converges absolutely?
Alternating series and absolute convergence are defined and explained with several examples. Some very interesting and helpful examples are included. The geometric series, alternating p-series, ratio test, and root test are used in finding absolute and conditional convergence. This is a very useful lecture in Calculus.
  • Currently 4.0/5 Stars.
Reviewed by MathVids Staff on December 20, 2008.
 
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