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Unformatted text preview: 1. If lim n !1 j a n +1 a n j = L < 1 ; then the series is absolutely convergent. 2. If lim n !1 j a n +1 a n j = L > 1 ; then the series is divergent. 3. If lim n !1 j a n +1 a n j = 1 ; then the Ratio Test is inconclusive. ex. 1 X n =1 3 n n ! 4 ex. 1 X n =1 2 n n 2 ex. 1 X n =1 1 n 3 5 NYTI: 1 X n =1 ( ± 1) n +1 n 2 2 n n ! ex. 1 X n =1 n 2 n Tonight’s homework: Practice Ratio test and work out problems to test for absolute or conditional convergence or divergence. Pay attention to which ones can’t be determined by applying ratio test . What do you do to determine the convergence of these problems? 6...
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 Spring '08
 Bonner
 Calculus

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