Pre-Calc Homework Solutions 366

Pre-Calc Homework Solutions 366 - 366 Section 9.1 1 1 2n...

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8. (a) We graph the points 1 n , } 1 1 2 1 2 2 n n } 2 for n 5 1, 2, 3, . [0, 23.5] by [ 2 2, 2] (b) lim n a n 5 lim n } 1 1 2 1 2 2 n n } 5 2 } 2 2 } 5 2 1 9. (a) We graph the points 1 n , 2 2 } 1 n } 2 for n 5 1, 2, 3, . [0, 23.5] by [ 2 1, 3] (b) lim n a n 5 lim n 1 2 2 } 1 n } 2 5 2 10. (a) We graph the points 1 n , } ln ( n n 1 1) } 2 for n 5 1, 2, 3, . [0, 23.5] by [ 2 1, 1] (b) lim n a n 5 lim n } ln ( n n 1 1) } 5 lim n 5 0 Section 9.1 Exercises 1. (a) Let u n represent the value of * in the n th term, starting with n 5 1. Then } u 1 1 } 5 1, 2 } u 1 2 } 5 2 } 1 4 } , } u 1 3 } 5 } 1 9 } , and 2 } u 1 4 } 5 2 } 1 1 6 } , so u 1 5 1, u 2 5 4, u 3 5 9, and u 4 5 16. We may write u n 5 n 2 , or * 5 n 2 . (b) Let u n represent the value of * in the n th term, starting with n 5 0. Then } u 1 0 } 5 1, 2 } u 1 1 } 5 2 } 1 4 } , } u 1 2 } 5 } 1 9 } , and 2 } u 1 3 } 5 2 } 1 1 6 } , so u 0 5 1, u 1 5 4, u 2 5 9, and u 3 5 16. We may write u n 5 ( n 1 1) 2 , or * 5 ( n 1 1) 2 . (c) If * 5 3, the series is ( 2 1) 3 1 } 2 1 2 1 } 2 1 ( 2 1) 4 1 } 2 2 2 1 } 2 1 ( 2 1) 5 1 } 2 3 2 1 } 2 1 ( 2 1) 6 1 } 2 4 2 1 } 2 1 , which is the same as the desired series. Thus let * 5 3.
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