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Unformatted text preview: comes to rest. Problem 4 (10 points): Determine which of the following series converges. For any that converge, ﬁnd the limit. (a): ∞ X n =1 ln ± 2 n 7 n5 ² (b): ∞ X n =1 (1) n 5 2 n (2 n )! (c): ∞ X n =1 ( 2n23 n ) Problem 5 (10 points): Find the ﬁrst four nonzero coeﬃcients of the MacLaurin series expansion of f ( x ) = ln(1 + x ) 1x . Problem 6 (10 points): (a): Find the interval of convergence for the power series ∞ X n =1 1 n 5 n ( x4) n (b): Give an example of two power series ∑ a n ( xc ) n and ∑ b n ( xc ) n with identical radius of convergence R such that the radius of convergence R of the series X ( a n + b n ) ( xc ) n satisﬁes R > R ....
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 Spring '10
 DONALDSON,NEIL
 Calculus, Power Series, Taylor Series, Mathematical Series

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