Determine if each of the following series converges

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16. Determine if each of the following series converges or diverges. For each series, state which test you use . (Note this problem continues on the next page.) (a) (4 pts) X n =1 1 cos( πn ) (b) (4 pts) X n =1 n ( n 2 + 4) 5 / 2 (c) (4 pts) X n =1 7 n e - 1
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Question 16 continues . . . Final Exam, Page 14 of 15 May 8, 2010 (d) (4 pts) X n =1 6 n 5 n - 1 17. Find the interval of convergence for each of the following series. (a) (3 pts) X n =1 3 n x n n 2 (b) (3 pts) X n =1 e n ( x - 5) n n !
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Final Exam, Page 15 of 15 May 8, 2010 18. (5 pts) Find Taylor series for f ( x ) = xe x +1 centered at x = 0. State the interval of convergence. 19. (6 pts) Use an appropriate Taylor series to find Z x 0 cos( t 2 ) dt . Express your answer as a summation (that is, with a Σ).
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