MTH 161 Final: MTH 161 University of Rochester 161 Final Spring 2007
31 Jan 2019
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Circle your instructor"s name along with the lecture time: Vermesi 9:00 mueller 10:00: no calculators are allowed on this exam, please show all your work. You may not receive full credit for a correct answer if there is no work shown: please put your simpli ed nal answers in the spaces provided. Express the following continued fraction as a rational number. If you can express it as the sum of two rational numbers, that"s also ok: (11 points) Answer: (b) (6 points) justify your answer in part (a): (12 points) Xn=1 ( 1)n 1 n2 (a) (3 points) does this series converge or diverge? (b) (4 points) justify your answer in part (a). Answer: (c) (5 points) suppose we approximate the series by taking the sum of the rst n terms, up to and including ( 1)n(1/n2). Answer: (b) (6 points) justify your answer, making sure to name any convergence tests that you are using: (11 points)
