Unformatted text preview: n →∞ a n = 0 3. Section 11.3 (a) The Integral Test: If f is continous, postive and decreasing on [1 , ∞ ) and let a n = f ( n ). If Z ∞ 1 f ( x ) dx is convergent then ∞ X n =1 a n is convergent. 4. Section 11.4 (a) Limit Comparison Test: Suppose that ∑ a n and ∑ b n are series with positive terms. If lim n →∞ a n b n = c > 0 then either both series converges or both series diverges. 5. Section 11.5 (a) The Alternating Series Test: If ∞ X n =1 (1) n b n where b n > 0 and (i) b n +1 ≤ b n for all n and (ii) lim n →∞ b n = 0 then the series is convergent. 6. Section 11.6 (a) If a series is absolutely convergent, then it is convergent....
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This note was uploaded on 07/11/2011 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.
 Spring '08
 Bonner
 Geometric Series

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