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Pre-Calc Homework Solutions 388

# Pre-Calc Homework Solutions 388 - 388 Section 9.5 2 n...

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19. Converges absolutely, since n 5 1 n 2 1 } 2 3 } 2 n converges by the Ratio Test: lim n ) } a a n 1 n 1 } ) 5 ( n 1 1) 2 1 } 2 3 } 2 n 1 1 ? } n 1 2 } 1 } 3 2 } 2 n 5 } 2 3 } , 1. 20. Converges conditionally. If u n 5 } n l 1 n n } , then { u n } is a decreasing sequence of positive terms with lim n u n 5 0, so n 5 2 ( 2 1) n 1 1 } n l 1 n n } converges by the Alternating Series Test. But n 5 2 } n l 1 n n } diverges by the integral test, since E 2 } x l 1 n x } dx 5 lim b 3 ln ) ln x ) 4 5 ‘ . 21. Diverges by the n th-Term Test, since lim n } 2 n n ! } 5 ‘ and so the terms do not approach 0. 22. Converges absolutely, since n 5 1 ) } si n n 2 n } ) converges by direct comparison to n 5 1 } n 1 2 } , which converges as a p -series with p 5 2. 23. Converges conditionally: If u n 5 } 1 1 1 ˇ n w } , then { u n } is a decreasing sequence of positive terms with lim n u n 5 0, so n 5 1 } 1 ( 1 2 1 ˇ ) n n w } converges by the Alternating Series Test.
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