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Unformatted text preview: Part 2: Sequence and Infinite Series 1. Find the interval of convergence for the following series (a) 1 2 n n n nx + = (b) ( 29 1 1 ! n n n n n x n =(c) ( 29 ( 29 2 1 1 2 1 n n n n x n + =+ (d) ( 29 1 1 10 ! n n n n x n + =(e) ( 29 ( 29 1 2 1 n n n n x n =+ (f) ( 29 2 1 4 1 n n n nx n = + 2. Determine the convergence or divergence of the following series (a) 3 1 3 2 n n n n = (b) ( 29 1 ! ! 2 ! n n n n = (c) ( 29 2 1 10 1 3 2 n n n n n = + + + (d) 1 cos 2 n n π = (e) ( 29 1 3 ! n n n =(f) ( 29 2 cos n n n = 3. Find the Taylor series for (a) 2 1 ( ) about 1 f x c x = = (b) ( ) ln about 2 f x x c = = 4. Determine whether the sequence converges or diverges. If converges, find the limit (a) { } 2 n a n n = +(b) ( 29 2 3 1 n n + (c) ! 2 n n n a = (d) 2 cos 2 n n n a = (e) ( 29 2 3 1 1 n n n a n = + (f) ( 29 1 n n(g) 2 2 2 1 5 3 n n n + +...
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This note was uploaded on 03/11/2012 for the course MATH 2J 44360 taught by Professor Donaldson,neil during the Spring '10 term at UC Irvine.
 Spring '10
 DONALDSON,NEIL

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