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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
- varies
- Calculus, Mathematical Series, arctann