APPM1360Fall07Test3 - APPM 1360 EXAM #3 FALL 2007 On the...

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APPM 1360 EXAM #3 FALL 2007 On the front of your bluebook, please write: a grading key, your name, student ID, and section and instructor (Dougherty, section 10, or Li, section 30 with lecture at 1 pm or section 20 with lecture at 2 pm). This exam is worth 100 points and has 5 questions. Show all work! Answers with no justification will receive no points. 1. (20 points) A few unrelated questions. Justify your answer in each case. (a) Does X n =1 1 1 + 2 + 3 + · · · + n converge or diverge? (b) Does X n =1 ( - 1) n n converge or diverge? (c) Find the limit: lim x 0 sin x - x + ( x 3 / 6) x 5 . 2. (30 points) Consider the series given by X n =2 x n n ln n Justify each answer carefully and completely. (a) What is the radius of convergence for this series? (b) For what values of x does the power series converge absolutely? (c) For what values of x does the power series converge conditionally (but not absolutely)? (d) For what values of
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