Notes on the Comparison Tests

Notes on the Comparison Tests - Notes on the Comparison...

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Unformatted text preview: Notes on the Comparison Tests There are two comparison tests. One is called The Comparison Test and the other one is called The Limit Comparison Test. Both tests require one to choose another series to which the given series is compared. During the course of the class, we will learn about certain well known series that you can use in this regard. So far we have learned about the p-series, which includes the Harmonic series. So these comparison tests work well when the given series looks a little like a p-series. The Comparison Test : Let n a ∑ and n b ∑ be two series of positive terms. Then a) If n b ∑ converges and n n a b ≤ for all n sufficiently large, then n a ∑ also converges. b) If n b ∑ diverges and n n a b ≥ for all n sufficiently large, then n a ∑ also diverges. The Limit Comparison Test : Let n a ∑ and n b ∑ be two series of positive terms. If lim n n n a C b →∞ = , where C is finite and positive, then either both series converge or both series diverge. There are several observations that one must keep in mind in applying these Comparison tests....
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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 Comparison Tests - Notes on the Comparison...

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