This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: n . If the limn anbn = L then, 1. If L = 0 and = n 0 bn converges then = n 0 an converges 2. If L > 0 then = n 0 an iff = n 0 bn converges Absolute Convergence an is called absolutely convergent if an converges Conditional Convergence an is called conditionally convergent if an converges and an diverges Leibniz Alternating Series Test Iff : i) a n > a n+1 and ii) = limn an 0 (a n converges to 0) Then the following alternating series is said to conditionally converge: = n 0 Qan , where Q is (1) n , (1) n+1 , (1) n1 , etc. Root Test = L limn nan i) If L < 1 then an converges absolutely ii) If L > 1 then an diverges iii) If L = 1 then the test fails and is inconclusive Ratio Test = + limn an 1an iv) If < 1 then an converges absolutely v) If > 1 then an diverges vi) If = 1 then the test fails and is inconclusive...
View
Full
Document
This note was uploaded on 10/12/2009 for the course MATH calculus 3 taught by Professor Ningzhong during the Spring '08 term at University of Cincinnati.
 Spring '08
 ningzhong
 Calculus, Geometric Series

Click to edit the document details