MATH 1272 Lecture 1: 11.4 The Comparison and Limit Comparison Tests
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Are series whose terms are all nonnegative. (an, bn 0 for all n) If series bn converges and an bn for all n, then series an converges. If series bn diverges and an bn for all n, then series an diverges. Note bn 0 for all n 1 and. We predict the series an converges, but we must finish using the theorem to prove it. We have met all conditions for part (a) except,we haven"t shown an bn for all n. We made the demo nematode smaller and everything is > 0, so quotient gets larger. So, by the comparison test, the series converges. *when using this test, we first look at dominating terms to make a prediction about convergence or divergence. That tells us if we need an . Bn or an bn to use the comparison test. A larger denominator makes a positive quotient smaller. Suppose series an and series bn are series with all positive terms.
