James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

704 Chapter 11 Infinite Sequences and Series
1. (a) What is a sequence?
(b) What does it mean to say that lim n l ` a n − 8?
(c) What does it mean to say that lim n l ` a n − `?
2. (a) What is a convergent sequence? Give two examples.
(b) What is a divergent sequence? Give two examples.
3–12 List the first five terms of the sequence.
3. a n − 2 n
2n 1 1
4. a n − n2 2 1
n 2 1 1
5. a n − s21dn21
5 n 6. a n − cos n 2
7. a n −
1
sn 1 1d!
9. a 1 − 1, a n11 − 5a n 2 3
10. a 1 − 6, a n11 − an
n
11. a 1 − 2, a n11 − an
1 1 a n
12. a 1 − 2, a 2 − 1, a n11 − a n 2 a n21
8. a n − s21dn n
n! 1 1
13–18 Find a formula for the general term a n of the sequence,
assuming that the pattern of the first few terms continues.
13. 5 1 2 , 1 4 , 1 6 , 1 8 , 1 10 , . . .6
14. 54, 21, 1 4 , 2 1
16 , 1 64 , . . .6
15. 523, 2, 2 4 3 , 8 9 , 216 27 , . . .6
16. h5, 8, 11, 14, 17, . . .j
17. 5 1 2 , 24 3 , 9 4 , 216 5 , 25 6 , . . .6
18. h1, 0, 21, 0, 1, 0, 21, 0, . . .j
19–22 Calculate, to four decimal places, the first ten terms of the
sequence and use them to plot the graph of the sequence by hand.
Does the sequence appear to have a limit? If so, calculate it. If not,
explain why.
23–56 Determine whether the sequence converges or diverges.
If it converges, find the limit.
23. a n − 3 1 5n2
n 1 n 2
25. a n −
n 4
n 3 2 2n
3 1 5n2
24. an −
1 1 n
26. a n − 2 1 s0.86d n
27. a n − 3 n 7 2n 28. a n − 3sn
sn 1 2
29. a n − e 21ysn 30. a n − 4n
1 1 9 n
31. a n −Î 1 1 4n2
1 1 n 2 S 32. an − cos n
n 1 1D
n 2
33. a n −
sn 3 1 4n
35. a n − s21dn
2sn
s2n 2 37. H
s2n 1 1d!J
34. a n − e 2nysn12d
36. a n − s21dn11 n
n 1 sn
38. H ln n
ln 2nJ
39. {sin n} 40. a n − tan21 n
n
41. hn 2 e 2n j 42. a n − lnsn 1 1d 2 ln n
43. a n − cos2 n
2 n 44. a n − s n 2 113n
45. a n − n sins1ynd 46. a n − 2 2n cos n
47. a n −S1 1
nD
2 n
49. a n − lns2n 2 1 1d 2 lnsn 2 1 1d
50. a n −
sln nd2
n
51. a n − arctansln nd
48. a n − s n n
19. a n − 3n
1 1 6n
21. a n − 1 1 (2 1 2) n
20. a n − 2 1 s21dn
n
22. a n − 1 1 10 n
9 n
52. a n − n 2 sn 1 1 sn 1 3
53. h0, 1, 0, 0, 1, 0, 0, 0, 1, . . . j
54. 5 1 1 , 1 3 , 1 2 , 1 4 , 1 3 , 1 5 , 1 4 , 1 6 , ...6
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