calculus 2 engineering 118

Calculus 2 - Wednesday February 8 Lecture 19 Tests for convergence of series Limit Comparison test(Refers to Section 8.4 in your text After having

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Wednesday, February 8 Lecture 19 : Tests for convergence of series : Limit Comparison test. (Refers to Section 8.4 in your text) After having practiced the problems associated to the concepts of this lecture the student should be able to : Apply the Limit comparison test to determine convergence or divergence of a series. 19.1 Theorem The Limit Comparison test . Suppose { a j : j = 1, 2, 3, …} and { b j : j = 1, 2, 3, …} are both sequences of non-negative terms. Then: Proof: 1. Suppose lim j → ∞ ( a j / b j ) = L > 0,
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2. Suppose lim j → ∞ ( a j / b j ) = 0, (For part 3: Remember lim j c j = means that for any integer N > 0 no matter how large, the interval [ N , ) contains a tail end of the sequence { c j }.) 3. Suppose lim j → ∞ ( a j / b j ) = . Let M be any positive integer. 19.2 Examples a ) Test for convergence the series Solution: Let Observe that when n is large a n only slightly distinguishes itself from b n = 3/ n 2 . Hence if we ignore the terms 1/
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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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Calculus 2 - Wednesday February 8 Lecture 19 Tests for convergence of series Limit Comparison test(Refers to Section 8.4 in your text After having

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