# prob11 - the root test in order to determine whether the...

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Math 151 Spring 2008 Problem Set # 11 The Ratio Test and the Root Test Starred Problems are due on Monday, April 14 In problems 1 - 18 use the ratio test in order to determine whether the given series converges absolutely or whether it diverges, provided that the test is applicable. You need not investigate the convergence of the given series if the test is inconclusive: 1*. X n =0 e n 2. X n =0 ( 1 . 1) n . 3. X n =0 3 n 4*. X n =0 ( 1) n 1 2 n . 5*. X n =0 3 n n ! 6*. X n =0 n ! 3 n 7. X n =0 ( 1) n 2 n n ! . 8*. X n =1 n 2 4 n 9. X n =1 ( 1) n 4 n n 2 10*. X n =2 ln( n ) n 2 11. X n =1 n n 2 +1 12*. X k =0 ( 1) k π 2 k +1 2 2 k +1 (2 k +1)! . 13. X n =1 ( 1) n 1 1 n 2 n . 14*. X n =1 ( 1) n 1 2 n n . 15*. X k =0 ( 1) k 1 2 2 k +1 (2 k +1) . 16. X k =0 ( 1) k 4 2 k +1 2 k +1 . 17*. X n =1 ( 1) n 1 n ln ( n ) 18. X k =0 ( 1) k 1 (1 . 1) k k . 1

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In problems 19 - 26 use
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Unformatted text preview: the root test in order to determine whether the given series converges absolutely or whether it diverges, provided that the test is applicable. You need not investigate the convergence of the given series if the test is inconclusive: 19. ∞ X n =1 10 n n n 20*. ∞ X n =1 n 2 2 n 21*. ∞ X n =2 ln( n ) n 3 22*. ∞ X n =1 n 4 e − n 23. ∞ X n =0 ( − 1) n 1 3 n . 24*. ∞ X n =0 ( − 1 . 5) n . 25. ∞ X n =1 ( − 1) n − 1 1 n 4 n . 26*. ∞ X n =1 ( − 1) n − 1 (1 . 2) n n . 2...
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prob11 - the root test in order to determine whether the...

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