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Unformatted text preview: 6. (12) a. Determine, with justiﬁcation, whether each of the following series converges. If any of the convergent series contains negative terms, distinguish between absolute and conditional convergence. i) ∞ ∑ n 2 1 n log n ii) ∞ ∑ n 1 1 n 1 n 1 n 2 iii) ∞ ∑ n 1 sin 1 n 2 1 (6) b. Suppose ∞ ∑ n 1 a n converges, where a n 0 for all n . Does ∞ ∑ n 1 a 2 n converge? Justify your answer or give a suitable counterexample. (15) 7. a. Express the function f x x t 2 sin t dt as a power series about a 0. b. What is the radius of convergence of the series ∞ ∑ n 1 nx n n ! 2 n ? (8) 8. Suppose x 3 f t dt x cos π x 6 . Compute f 8 . 2...
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This note was uploaded on 10/14/2010 for the course MAT MAT taught by Professor Unknown during the Spring '10 term at Touro CA.
 Spring '10
 unknown
 Calculus

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