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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) n-1 , 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...
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