Lesson 25a - Ratio and Root Test

Thisisageometricseriestheconverges

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Unformatted text preview: t it is a geometric series with L < 1. This is a geometric series the converges. Thus by the comparison test the original series is absolutely convergent. | an | Ln | ak | For L > 1, the proof is identical except we have , but the series nk nk on the right is divergent (geometric series L > 1). By comparison, the original diverges as well. Root Test Given a series , then consider the limit: lim an an n n 1 1/ n L Then we have the following: 1. If L < 1, then converges absolutely. (notice the absolute value) an n 1 2. If L > 1, then diverges. an n 1 3. If L = 1, then the test fails. Root Test Proof Given a series , then consider the limit: lim an an n n 1 1/ n L 1 n This means that eventually we will ha...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

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