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Unformatted text preview: verify that the conditions necessary to apply the test are met. (a) X (-1) k 1 + 2 ln k (b) X (-1) k ( k-1) k + k 3 (c) X (-1) k (3 k )! k !(2 k )! (d) X (-1) k ( k- k-1) k 2. Find the smallest integer n so that the n th partial sum s n approximates the sum of the series X k =1 (-1) k +1 k 3 with error less than 0.0001. 3. (a) Explain clearly why it must be true that if X a k converges absolutely, then X ( a k ) 2 converges. (b) Give examples to show that if X ( a k ) 2 converges, then X a k may con-verge or may diverge. (In other words, the convergence of X ( a k ) 2 gives no information about the convergence of X a k .) 1...
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This note was uploaded on 10/14/2009 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas at Austin.
- Spring '07