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How Does Limit Comparison Test Work

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The limit comparison test shows that the original series is convergent. Because 1 is a finite positive number we are in case i of the limit comparison test. The Limit Comparison Test Youtube The limit comparison test does not apply because the limit in question does not exist. . Because our limit converged to a nite non-zero constant we may. Lim x1 fx gx lim x1 xx2 p x 1 1x lim x1 x2 x2 p x 1 1. Where a n 0 and b n 0. Indeed lim n1 a n b n lim n1 np 21sinn 7 51 pn2 n7 lim n1 1 1 n2 sinn q 1 1 n5 n7 100 p 100 1. If the test does not apply say so. Thats why there are so many of them. The idea behind the limit comparison test is that if you take a known convergent series and multiply each of its terms by some number then that new series also converges. Thus the LCT tells us that R 1 2 fxdxmust also diverge. Using the Ratio Test The real utility of this test is that one need not know about another series to det...
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