11.6 Absolute Convergence and the Ratio Test - Math 1132...

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Math 1132 Worksheet 11.6 Name:Discussion Section:11.6 Absolute Convergence and the Ratio TestAbsolute Convergence.A seriesanis called absolutely convergentif the series of theabsolute values|an|is convergent.Note: If a series is absolutely convergent then it is also convergent.Conditional Convergence.A seriesanis called conditionally convergentif it is con-vergent but not absolutely convergent.The Ratio Test.(i) If limn→∞an+1an=L <1, then the seriesXn=1anis absolutely convergent (and thereforeconvergent).(ii) If limn→∞an+1an=L >1 or limn→∞an+1an=, then the seriesXn=1anis divergent.(iii) If limn→∞an+1an= 1, the Ratio Test is inconclusive; that is, no conclusion can be drawnabout the convergence or divergence ofXn=1an.Factorial.n! =n·(n-1)·(n-2)·(n-3)· · · · ·5·4·3·2·1.
1.Example:Determine if the series is absolutely convergent, conditionally convergent, ordivergent.

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