## The Integral Test

The Integral Test
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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.
The integral test for convergence of series with positive terms; p-series. Remainder estimation.
• What is the integral test for series?
• What are p-series?
• What is the harmonic series?
• When does a p-series converge or diverge?
• Does 1/klnk from k = 2 to infinity converge or diverge?
• Does 1/k(lnk)^2 from k = 2 to infinity converge or diverge?
• What is the nth remainder of a convergent series?
• How can you estimate the remainder of a series?
• How can you use partial sums to estimate the sum of an infinite series to an error of less than 0.01?
• How do you use partial sums to approximate the sum of k/2^k?
The Integral test for determining whether a series is convergent or divergent is given and explained using animations. The harmonic series, which is a special case of p-series, is defined. Also, the p-series test for convergence is explained. Partial sums are used to approximate sums of infinite series to less than a specific error.
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Reviewed by MathVids Staff on December 20, 2008.