Pre-Calc Homework Solutions 389

Pre-Calc Homework Solutions 389 - Section 9.5 an an xn(n 1...

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Unformatted text preview: Section 9.5 an an xn (n 1) n n n 1 389 33. lim n 1 lim n n 1 3n 1 n 3n x n x 3 38. lim n an an 1 lim n (n 1)! x 4 n n! x 4 n 1 The series converges absolutely for x when x 3, x n 3. Furthermore, lim (n n 1) x 4 4 4 n 1 as a p-series with p (a) [ 3, 3] (b) [ 3, 3] (c) None 34. lim n n3 3 . 2 1 n1 , which also converges 3/2 n (a) Only at x (b) At x (c) None 39. lim n 0, x , x 4 4 an an 1 lim n 2 n 1(n 2 n(n 2) x 1) x 1n 1n 1 2(x 1) 1) 1, or an an 1 lim n x (n 2n 3 1)! n! x 2n 1 lim n x n 2 1 0 The series converges absolutely for 2(x 1 2 The series converges absolutely for all real numbers. (a) All real numbers (b) All real numbers (c) None 35. lim x 3 5n 5 nx 3n n n x 3 The series converges absolutely for 1, 5 x 3 or 8 x 2. For 1, the series diverges by 5 an 1 x 3 . For 2(x 2 1) 1, the series diverges by the nth-Term Test. (a) 1 3 , 2 2 1 3 , 2 2 an lim (n 1) x 5n 3n 1 1 (b) (c) None 40. lim n an an 1 lim n the nth-Term Test. (a) ( 8, 2) (b) ( 8, 2) (c) None 36. lim n 4x (n 5 2n 3 1)3/2 4x n 3/2 5 2n 2n 1 1 (4x 5)2 5)2 The series converges absolutely for (4x 3 . Check x 2 1, or 1 an an 1 (n 1) x n 4n 1[(n 1)2 n 1 lim 1] x 4 4n(n2 1) nxn x 4 ( 1) 1 x 1: n3/2 n 1 n 3 converges as a p-series with p . Check x 2 12n 1 3 . 3/2 converges as a p-series with p 2 n 1 n 1 n3/2 3 : 2 The series converges absolutely for Check x n 1, or 4 x 4. (a) 1, (b) 1, 3 2 3 2 4: n 0 n (n2 1) 1 converges by the Alternating Series Test. (c) None 41. lim n Check x 4: diverges by the Limit Comparison Test an an 1 lim n x n n 1 n x n x 1, or n 0 n2 n n 1 with 1 1 . 1 n The series converges absolutely for x 1 Check x x 1: n 1. (a) [ 4, 4) (b) ( 4, 4) (c) At x 37. lim n 4 lim n n 1 ( 1 1) n converges by Alternating Series Test. 1: 1 . 2 an an 1 n 3n 1 xn 1 1 Check x 3n n xn x 3 n 1 diverges as a p-series with p n The series converges absolutely for x For x 3, or 3 x 3. (a) [ (b) ( (c) At x 1, 1, 1 1) 1) 3, the series diverges by the nth-Term Test. (a) ( 3, 3) (b) ( 3, 3) (c) None ...
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