MAC 2312 Lecture 21: Lectures 21-30
16 Dec 2017
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Lecture 21: absolute convergence and the ratio test (11. 6) Consider the two convergent alternating series (a) x ( 1)n n and (b) x ( 1)n n2. Consider the series whose terms are the absolute values of the terms of the original series: Since x 1 diverges and the original series (a) coverges, we say that (a) is conditionally con- vergent. n. Since x 1 n2 converges, we say that (b) is ab- solutely convergent. X n=1 an is absolutely conver- gent if the series. In other words, a series is absolutely conver- gent if the series of absolute values is conver- gent. If x an converges, but x |an| diverges, then it converges conditionally. In other words, a series is conditionally con- vergent if it is convergent, but not absolutely convergent. I consider land . in . by. I. me#fi. e divers (conv. ) his answer oeth eek and since by ftest ,
