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Unformatted text preview: Version 058 DGQ04 gilbert (55485) 1 This printout should have 4 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. MAKE SURE you BUBBLE in your EID AND EXAM VERSION 001 10.0 points Determine whether the series summationdisplay m =1 ( 6) m +1 5 3 m is absolutely convergent, conditionally con vergent or divergent. 1. conditionally convergent 2. absolutely convergent correct 3. divergent Explanation: The given series can be written in the form summationdisplay m =1 ( 6) m +1 5 3 m = summationdisplay m =1 a n with a m = ( 1) m +1 6 m +1 5 3 m = ( 1) m +1 6 parenleftBig 6 5 3 parenrightBig m . But then vextendsingle vextendsingle vextendsingle a m +1 a m vextendsingle vextendsingle vextendsingle = 6 5 3 ; in particular, lim m vextendsingle vextendsingle vextendsingle a m +1 a m vextendsingle vextendsingle vextendsingle = 6 5 3 < 1 ; Consequently, by the Ratio Test, the given series is absolutely convergent ....
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This note was uploaded on 05/02/2011 for the course M 408 D taught by Professor Textbookanswers during the Spring '07 term at University of Texas at Austin.
 Spring '07
 TextbookAnswers

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