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A8 - Schedule and exercise list sheet found on the ACE...

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MATH 138 Winter 2011 Assignment 8 Topics: Comparison test, alternating series test. Due: 11 a.m. Friday, March 11. Instructions: Print your name and I.D. number at the top of the first page of your solutions, and underline your last name. Submit your solutions in the same order as that of the questions appearing herein. On collaboration: First attempt the questions on your own, but if you get help or collaborate with someone, then acknowledge the names of those who helped you. Any outright copying of assignments will be reported as an act of academic plagiarism. On work presentation: Your solutions must have legible handwriting, and must be presented in clear, concise and logical steps that fully reveal what you are doing. Questions such as those to be handed in, as well as those that are recommended, may appear on exams. To avoid frustration and disappointment, get started on your assignment early. Do not forget to work on the recommended problems from Stewart’s book that are
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Unformatted text preview: Schedule and exercise list sheet found on the ACE webpage. This will give you much needed practice. Hand in your solutions to the following problems. 1. Determine whether each of the following series is convergent or divergent. (a) ∞ X n =1 2 n 3 n + 1 (b) ∞ X n =1 n + 5 3 √ n 7 + n 2 (c) ∞ X n =1 3 1 /n n 4 1 (d) ∞ X n =1 sin ± 1 n ² (e) ∞ X n =1 n ! n n 2. Determine whether each of the following alternating series is convergent or diver-gent. (a) ∞ X n =1 (-1) n-1 e 1 /n n (b) ∞ X n =3 (-1) n-1 ln n n (c) ∞ X n =1 (-1) n-1 cos ± 1 n ² 3. Explain briefly why each series below converges. Then find n such that the n th partial sum s n will approximate the full sum s with error less than the amount specified. Then use your calculator to actually compute that approximation. (a) s = ∞ X n =1 (-1) n-1 1 n 3 , with error less than . 01 . (b) s = ∞ X n =1 (-1) n-1 2 n n ! , with error less than 1 / 10 4 . 2...
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