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
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.
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