lec 17 - Monday, February 6 - Lecture 17 : Integral test,...

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Lecture 17 : Integral test, p-series. (Refers to Section 8.3 in your text) After having practiced the problems associated to the concepts of this lecture the student should be able to : State the Integral test and apply it to determine whether an appropriate series converges or diverges, recognize a p -series and state when it converges and when it diverges. 17.1 Theorem The integral test . Let be a series with non-negative terms decreasing in size. Suppose f ( x ) is a positive , decreasing , continuous function on [1, ) such that f ( i ) = c i for all i . Then the series converges if and only if the improper integral converges. To prove the theorem it suffices to show that The details are given in class. 17.1.1 Remarks – In the case of convergence the integral test gives no indication as to the value of the limit of the series in question. 17.1.2 Example Does the series provides no info on convergence
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This note was uploaded on 03/19/2012 for the course MATH 118 taught by Professor Zhou during the Winter '08 term at Waterloo.

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lec 17 - Monday, February 6 - Lecture 17 : Integral test,...

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