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Unformatted text preview: (5%) b. Suppose a n 1 2 for all n . Find the radius of convergence for the power series of f x . 1 (6%) c. Using parts (a) and (b), compute the exact value of the sum ∞ ∑ n n 2 n (Recall that n 2 n n 1 2 n .) 6. Suppose f x M for all x a b , where M is some constant. (4%) a. Apply a theorem to show that f b f a M b a (5%) b. Use part (a) to show that log 66 log8 1 64 (8%) 7. Suppose ∞ ∑ n 1 a n and ∞ ∑ n 1 b n are two series that both converge, and a n b n 0 for all n . Must the series ∞ ∑ n 1 a n b n also converge? Justify your answer with an appropriate proof or counterexample. (8%) 8. Give the εN definition of the statement a n converges to L Prove, using the definition, that the sequence a n defined by a n n n 3 1 converges to zero. 2...
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 Spring '10
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 Calculus, Derivative, Power Series, Convex function, April/May Examinations MAT

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