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Unformatted text preview: Jonathan Kim Assignment A6 MATH141, Winter 2008 You may attempt each problem a maximum of 5 times. Please remember that, while WeBWorK can usually check only the correctness of your answers, your responsibility in this course is to be able to justify your answers to problems of all these types, and others. The assignment is due Sunday, April 6, 2008, at 11:30 PM. 1. (1 pt) Consider the series ∑ ∞ n 1 a n where a n 1 n n 2 5 n 4 In this problem you must attempt to use the Ratio Test to decide whether the series converges. Compute L lim n ∞ a n 1 a n Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L Which of the following statements is true? A. The Ratio Test says that the series converges absolutely. B. The Ratio Test says that the series diverges. C. The Ratio Test says that the series converges conditionally. D. The Ratio Test is inconclusive, but the series converges ab- solutely by another test or tests. E. The Ratio Test is inconclusive, but the series diverges by an- other test or tests. F. The Ratio Test is inconclusive, but the series converges con- ditionally by another test or tests. Enter the letter for your choice here: Correct Answers: 1 D 2. (1 pt) Find the value of ∞ 2 dx 4 x ln 2 x 2 Determine whether ∑ ∞ n 2 1 4 n ln 2 n 2 is a convergent series. Enter CONV if the series is convergent, DIV if the series is divergent....
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