This file is part of a distribution of the Calculus Applets website (http://www.calculusapplets.com) (v1.1) which has been reformatted for the needs of this OpenCourseware course.
The integral test provides another means to testing whether a series converges or diverges. Suppose we have a sequence defined by an = f (n), where f is some function, and we want to know whether the series converges or diverges. If f is positive, decreasing and continuous for x > c, then if converges the series also converges. If the integral diverges then so does the series. Hence if we can integrate f, and if there is some c for which f is positive, decreasing and continuous for x > c, then we can use this test. c = 1 is the most commonly selected c to use, but depending on the function you may have to use a larger c.
Try the following:
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© Copyright 2001 David J. Eck
© Copyright 2007 Thomas S. Downey
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