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Unformatted text preview: lim n a n + a 1 n + 1 + a 2 n + 2 + + a p n + p = 0 . 5. Discuss the convergence behavior oF the Following series stating in each case whether the series is absolutely convergent, conditionally conver-gent, or divergent: (a) X n =1 1 n ! . (b) X n =3 n ( n + 1)( n + 2) ( n + 3) 3 . (c) X n =1 1 + 1 n 2 n 2 . (d) X n =1 (-1) n n . 3 6. Give an example, if possible, of each of the following. If no example is possible, brieFy give reasons why: (a) A sequence a n 0, such that n =1 a n n diverges. (b) A sequence a n 0, such that n =1 a n n 2 diverges. (c) A series a n which converges such that a 2 n diverges....
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- Fall '08
- Real Numbers