Comparison Tests
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Lesson Summary:
In this lesson on Comparison Tests, students learn about the ratio and root tests as well as comparisons with p series. They also learn how to determine if a series converges or diverges by using either the ratio or root test, and they explore examples of each. Additionally, students learn how to compare a series with a geometric series and how to apply the limit comparison test.
Lesson Description:
Comparison and limit-comparison tests. The ratio and root tests.
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.
Questions answered by this video:
- What are comparison tests?
- What is the ratio test for convergence?
- What is the root test for convergence?
- What are some series that converge?
- What are some series that diverge?
- What is the limit comparison test?
- Does the sum of k^3/2^k converge or diverge?
- Does the sum of 1/square root of k! converge or diverge?
- Does the sum of k^2*2^k/k! converge or diverge?
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Staff Review
The basic idea of comparison tests is explained starting from the series we know so far. The video starts off and shows some examples of the comparison test with p-series and geometric series. Then, the limit comparison test, the ratio test, and the root test are explained. Several examples of each type of test are shown and explained. -
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Even though I understood some, the examples skip some steps and assumes that the viewer understands several of the algebraic "adjustments" that are used. Review of those will make this vid clearer. Comprehensible otherwise. Understand that he mentions limits but does not always have that on the screen. Going through the video twice helped
