math15 - Math 2153 Exam III Name Score Read the problems...

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Unformatted text preview: Math 2153, Exam III, April 23, 2010 Name: Score: Read the problems carefully before you begin. Show all your work neatly and concisely, and indicate your final answer clearly. Total points = 50. 1. (8 points) Find the interval of convergence of the series ∞ summationdisplay n =1 (- 1) n ( x + 8) n n 6 n Solution By the ratio test lim n →∞ vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle (- 1) n +1 ( x +8) n +1 ( n +1)6 n +1 (- 1) n ( x +8) n n 6 n vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = lim n →∞ vextendsingle vextendsingle vextendsingle vextendsingle (- 1) n ( x + 8) 6( n + 1) vextendsingle vextendsingle vextendsingle vextendsingle = vextendsingle vextendsingle vextendsingle vextendsingle x + 8 6 vextendsingle vextendsingle vextendsingle vextendsingle < 1 ⇒ | x + 8 | < 6 ⇒- 14 < x <- 2 When x =- 14 , the series becomes ∞ summationdisplay n =1 (- 1) n (- 6) n n 6 n = ∞ summationdisplay n =1...
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math15 - Math 2153 Exam III Name Score Read the problems...

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