# HW9 (1) - HW9 Username Total Posted Due hairer-established...

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HW9 Username: hairer-established Total: 85 possible marks Posted: 2011-07-21 15:05 Due: 2011-07-29 23:59 1. (10 marks) Determine whether the following series is convergent or divergent. X n =1 1 n 4 n 7 + 1 a) Convergent b) Divergent 2. (10 marks) Determine whether the series X n =0 a n x n converges for 0 x 1 . Assume that a n > 0 for all n and X n =0 a n converges. a) Convergent b) Divergent 1

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3. (20 marks) Sum the following series or show that they are divergent. If it is divergent, enter ”DNE”; if it is convergent, give its sum. a) 1 1 + 1 3 + 1 5 + 1 7 + ··· ; b) 1 5 + 3 10 + 9 20 + 27 40 + 81 80 + ··· 2
4. (10 marks) a. Determine whether the series X n =1 ( - 1) n - 1 ln n n converges. b. If so, estimate the error if S 10 is used to approximate the sum of the series. If not, enter ”DNE” for your answer. a) Convergent b) Divergent a 11 = 3

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5. (15 marks) Determine whether each series is convergent or divergent. If the series is convergent,

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HW9 (1) - HW9 Username Total Posted Due hairer-established...

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