Unformatted text preview: 366 Section 9.1
1 1 2n for n 2n 1 ,a 3 2 1 , and so on. Thus 9 8. (a) We graph the points n, 1, 2, 3, ... . 2. (a) Note that a0 an
1 n . 3 1, a1 (b) Note that a1 an
[0, 23.5] by [ 2, 2] 1, a2
1 ( 1)n n 1 ,a 2 3 1 , and so on. Thus 3 . 5, a1
5 . 10n 1 n 1 alternate 2 (b) lim an
n 1 n 1 lim 2n 2n 2 2 1
1 for n n (c) Note that a0 an 1, 2, 3, ... . 5(0.1)n 0.5, a2 0.05, and so on. Thus 9. (a) We graph the points n, 2 3. Different, since the terms of n 1 between positive and negative, while the terms of
n 1 1 n 1 are all negative. 2 [0, 23.5] by [ 1, 3] 4. The same, since both series can be represented as
1 n (b) lim an
n lim 2
n 2
ln (n 1) for n n 1 1, 2, 3, ... . 1 2 1 4 1 8 .... 10. (a) We graph the points n, 5. The same, since both series can be represented as 1
1 2 1 4 1 8 ....
1 n 1 1 1 2 2 1 1 1 .... 2 4 8 1 1
2 3 5 4 6. Different, since [0, 23.5] by [ 1, 1]
1
n 1 ( 1) 2n 1 n n 1 1 4 1 8 ... but 1 (b) lim an
n ln (n 1) lim n n lim
n (n 1) 1 0 7. Converges; n 0 2 n 3 3 Section 9.1 Exercises
1. (a) Let un represent the value of * in the n th term, starting with n and u1 un
1 u4 8. Diverges, because the terms do not approach zero. 9. Converges; 5 4 2 n 3
2 3 3 n 0 1 5 4 15 4 1. Then 1 , so 16 1 u1 1, 1 u2 1 1 , 4 u3 1 , 9 10. Diverges, because the common ratio is do not approach zero. 1 and the terms 1 1, u2 n2, or * 4, u3 n2. 9, and u4 16. We may write 11. Diverges, because the terms alternate between 1 and and do not approach zero. 12. Converges; 3( 0.1)n
n 0 1 3 ( 0.1) 30 11 (b) Let un represent the value of * in the nth term, starting with n
1 u3 0. Then 1 , so u0 16 1 u0 1, 1, u1 1 u1 1 1 , 4 u2 1 , and 9 13. Converges; sin n
n 0 4 1 2
2 n
3 4, u2 (n 9, and 1)2, or * (n 1)2. 1
1 2
1 u3 (c) If * 16. We may write un 3, the series is
1 1 4
2 1 2 ... ( 1)3 ( 1)6 ( 1)4 1 2
2 ( 1)5 1 3
2 n 0 1 2 2( 2 n 1 1 1) 1)
1 2 2 2 2 1 1
2 ... , which is the same as the desired 3. 2 2 1 ( 2 1)( 2 2 2 series. Thus let * 14. Diverges, because the terms do not approach zero. ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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