Absolute convergence - Week 12 Class notes Section 11.6...

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Week 12 Class notesSection 11.6 - Absolute Convergence andthe Ratio and Root TestsA seriesanis called absolutely convergentif the series of absolute values|an|is con-vergent.A seriesanis called conditionally conver-gent if it is convergent but not absolutelyconvergent.If a seriesanis absolutely convergent, thenit is convergent.Ratio Test:(i) Iflimn→∞|an+1an|=L <1, then the seriesXn=1anis absolutely convergent and thus con-vergent.1
(ii) Iflimn→∞|an+1an|=L >1 orlimn→∞|an+1an|=, then the seriesXn=1anis divergent.(iii) Iflimn→∞|an+1an|= 1, then the Ratio Testis inconclusive.Root Test:

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