### 4 videos in "Tests for Convergence"

## 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.

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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.