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Notes on the Integral Test

# Notes on the Integral Test - Notes on the Integral Test The...

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Notes on the Integral Test The Integral Test is a method for determining the convergence or divergence of a series of positive terms. It has the advantage that, unlike some of the other tests we will discuss, it always provides an answer to the question of convergence. The drawbacks are: 1) there are a number of conditions that must be satisfied in order to apply the test; 2) one must be able to evaluate an improper integral, which may be difficult to accomplish for a given series. The Integral Test : Let n a denote a given series for which the terms of the series are eventually all positive. Suppose that f is a function for which ( 29 n f n a = for all large values of n . Furthermore suppose that f is positive, continuous, and decreasing on some interval [ 29 , M . Then n a converges if and only if the improper integral ( 29 M f x dx converges. There are several observations that one must keep in mind when applying the Integral Test. A. While it does not matter about the first few terms of the series, eventually all of the terms n a must be nonnegative. Most of the time the series will be a series of

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Notes on the Integral Test - Notes on the Integral Test The...

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