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# Q4 - Version 058 DGQ04 gilbert(55485 This print-out should...

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Version 058 – DGQ04 – gilbert – (55485) 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. MAKE SURE you BUBBLE in your EIDANDEXAMVERSION 001 10.0points 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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