Transcription of Lecture 26 : Comparison Test
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Lecture 26 : Comparison Test
Comparison Test Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Limit Comparison Test Example Example Example Example Example ExampleComparison TestIn this section, as we did with improper integrals, we see how to compare aseries (with Positive terms) to a well known series to determine if it convergesor will of course make use of our knowledge ofp-series and geometricseries. Xn=11npconverges forp>1,diverges forp 1. Xn=1arn 1converges if|r|<1,diverges if|r| TestSuppose thatPanandPbnare serieswith positiveterms.(i) IfPbnis convergent andan bnfor alln, thanPanis alsoconvergent.(ii)IfPbnis divergent andan bnfor all n, thenPanis PilkingtonLecture 26 : Comparison TestComparison Test Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Limit Comparison Test Example Example Example Example Example ExampleComparison TestIn this section, as we did with improper integrals, we see how to compare aseries (with Positive terms) to a well known series to determine if it convergesor will of course make use of our knowledge ofp-series and geometricseries.
arn 1 converges if jrj<1; diverges if jrj 1: I Comparison Test Suppose that P a n and P b n are series with positive terms. (i) If P b n is convergent and a n b n for all n, than P a n is also convergent. (ii) If P b n is divergent and a n b n for all n, then P a n is divergent. Annette Pilkington Lecture 26 : Comparison Test
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