Notes on the Ratio Test 1

Notes on the Ratio Test 1 - Notes on the Ratio Test The...

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Notes on the Ratio Test The Ratio Test provides a method to verify a given series converges absolutely. Unlike most of our previous tests, it applies to any series. Since absolute convergence implies convergence, the Ratio Test may be useful in showing a series converges. The drawback is that it sometimes fails to provide an answer. The Ratio Test : Let n a be a given series. Then a) If 1 lim 1 n n n a L a + →∞ = < , then n a converges absolutely (and therefore converges); b) If 1 lim 1 n n n a L a + →∞ = , or 1 lim n n n a a + →∞ = ∞ , then n a diverges; c) If 1 lim 1 n n n a a + →∞ = , no information for n a is provided by this test. There are a couple of observations that one must keep in mind when applying the Ratio Test. A. One takes a limit of the absolute value of the ratio of two consecutive terms. B. The test may not provide any information about the given series. C. In general the Ratio Test does not provide a way to estimate the error

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This note was uploaded on 05/06/2011 for the course MATH 256 taught by Professor Buekman during the Spring '11 term at Purdue.

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Notes on the Ratio Test 1 - Notes on the Ratio Test The...

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