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Unformatted text preview: (p.735) (i) If lim n →∞ n q  a n  = L < 1, then the series ∑ ∞ n =1 a n is absolutely convergent (and therefore convergent). (ii) If lim n →∞ n q  a n  = L > 1, then the series ∑ ∞ n =1 a n is divergent. Remark: If lim n →∞ n q  a n  = 1, then the Root Test gives no information. The series ∑ a n could converge or diverge. (If L = 1 in the Root Test, don’t try the Root Test because L will again be 1.) 1 11.6.14 ∞ X n =1 (1) n arctan n n 3 2 11.6.16 ∞ X n =1 (1) n +1 n 2 2 n n ! 3 11.6.24 ∞ X n =1 (1) n n ln n 4 11.6.14 ∞ X n =1 (1) n (arctan n ) n 5...
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 Spring '08
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 Calculus, Mathematical Series, arctann

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