408DS09assign3 - verify that the conditions necessary to...

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M408D Spring 2009 Assignment 3 Due Thursday, February 12 Be sure that you have read and understood sections 12.4, 12.5, and 12.6 and worked the assigned text exercises before you complete this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Homework is to be turned in at the beginning of the discussion section. 1. Determine whether each of the series below converges absolutely, converges conditionally, or diverges. In each case, state which test you are using and
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Unformatted text preview: verify that the conditions necessary to apply the test are met. (a) X (-1) k 1 + 2 ln k (b) X (-1) k ( k-1) k + k 3 (c) X (-1) k (3 k )! k !(2 k )! (d) X (-1) k ( k- k-1) k 2. Find the smallest integer n so that the n th partial sum s n approximates the sum of the series X k =1 (-1) k +1 k 3 with error less than 0.0001. 3. (a) Explain clearly why it must be true that if X a k converges absolutely, then X ( a k ) 2 converges. (b) Give examples to show that if X ( a k ) 2 converges, then X a k may con-verge or may diverge. (In other words, the convergence of X ( a k ) 2 gives no information about the convergence of X a k .) 1...
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This note was uploaded on 10/14/2009 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas at Austin.

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