Unformatted text preview: or conditionally convergent. You must give correct reasons for your answers to receive credit. (a) ∞ s n =1 (1) n 3 2 n n 3 2 3 n (b) ∞ s n =1 e√ n √ n (c) ∞ s n =1 (1) n sin(1 /n ) (d) ∞ s n =1 ( n !) 2 (2 n )! 4. (8 points) Let ∑ a n x n be the Maclaurin series for f ( x ) and let ∑ b n x n be the Maclaurin series for f (x ). (a) Express b n in terms of a n . (b) Suppose f ( x ) is an even function; that is, f (x ) = f ( x ). Show that, whenever n is odd, a n = 0. END OF EXAM...
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 Fall '06
 Mohanty
 Math, Differential Equations, Equations, Maclaurin Series, Taylor Series, Mathematical Series, blue book, correct reasons

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