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Pre-Calc Homework Solutions 392

Pre-Calc Homework Solutions 392 - 392 Chapter 9 Review x 4...

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58. continued (b) lim n ˇ n ) a w n ) w 5 lim n ! n § 5 lim n } ˇ ) n x n w 2 ? 2 3 ) } 5 } ) x 2 3 2 ) } The series converges absolutely if } ) x 2 3 2 ) } , 1, or 2 1 , x , 5. Check x 5 2 1: n 5 1 } ( 2 n 1) n } converges. Check x 5 5: n 5 1 } 1 n } diverges. The interval of convergence is [ 2 1, 5). (c) lim n ˇ n ) a w n ) w 5 lim n ˇ n 2 w n ) w x ) w n w 5 2 ) x ) The series converges absolutely if 2 ) x ) , 1, or 2 } 1 2 } , x , } 1 2 } . Check x 5 2 } 1 2 } : n 5 1 ( 2 1) n diverges. Check x 5 } 1 2 } : n 5 1 1 diverges. The interval of convergence is 1 2 } 1 2 } , } 1 2 } 2 . (d) lim n ˇ n ) a w n ) w 5 lim n ˇ n ) ln w x w ) n w 5 ) ln x ) The series converges absolutely if ) ln x ) , 1, or } 1 e } , x , e . Check: x 5 } 1 e } : n 5 0 1 ln } 1 e } 2 n 5 n 5 0 ( 2 1) n diverges. Check x 5 e : n 5 0 (ln e ) n 5 n 5 0 1 n diverges. The interval of convergence is 1 } 1 e } , e 2 . Chapter 9 Review Exercises (pp. 509–511) 1. lim n ) } a a n 1 n 1 } ) 5 lim n } ( ) n 2 1 x ) n 1 1) 1 !
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