3a.408DF11assign3 - X k =1 1 k 2 + 1 by a partial sum s n ....

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M408D Fall 2011 Assignment 3 Due Friday, September 16 Be sure that you have read and understood sections 12.3, 12.4, and 12.5 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 class. 1. Find all values of p for which X n =1 ln n n p converges. 2. We want to approximate the sum of the series
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Unformatted text preview: X k =1 1 k 2 + 1 by a partial sum s n . What is the smallest value of n for which s n approximates the sum with error less than 0.001? 3. (a) Explain clearly why it must be true that if X | a k | converges, 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 .) 4. 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. 1...
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