bz In Exercises 15-28, use Theorem 1 to determine the limit of the sequence or state that the sequence diverges. 15) an = 5-2n 5n 4 n2 4+n-3n² 16. an 20- -

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Can you help me solve 15? Theorem 1 says that a_n= f(n).
ero?
• Bounded monotonic sequences converge (Theorem 6).
(¹)"
F. That is, a₁ = 1,
(c)
vely?
timi
her og
terms of
rting
(b) b = √√√4+bn-1
5.
Theorem 5 says that every convergent sequence is bounded. Deter-
mine if the following statements are true or false, and if false, give a coun-
terexample:
(a) If (an) is bounded, then it converges.
(b) If [an] is not bounded, then it diverges.
(c) If (an) diverges, then it is not bounded.
(a) an = √4+n
14. Suppose that lim an = 4 and lim bn = 7. Determine:
848
818
(a) lim (an + bn)
848
(c) lim cos(лbn)
818
17, bn =
In Exercises 15-28, use Theorem 1 to determine the limit of the sequence
or state that the sequence diverges.
13
oryang art nl
15) an = 5 - 2n
12581/1)-n
drive (19. an = 252
21. Cn = 9n
23. an =
25. an In
27. Zn =
5n -1
12n +9
29, an=
√n² +1
n
4+
12n+2
-9+4n
n
(b) lim a
1148
screa
mil straw 3
(d) lim (a-2anbn)
818
TH
18. an =
16. an 20-
20. Zn =
n+1
en
28. yn = ne¹/n
900Sunga
In Exercises 29-32, use Theorem 4 to determine the limit of the sequenc
=e4n/(3n+9)
4
-n²
4+n-3n²
4n² +1
n
(3)
10-1/n
22. Zn =
24. an =
n
√n³+1
26. rn = Inn - In(n² + 1)
30. an
Transcribed Image Text:ero? • Bounded monotonic sequences converge (Theorem 6). (¹)" F. That is, a₁ = 1, (c) vely? timi her og terms of rting (b) b = √√√4+bn-1 5. Theorem 5 says that every convergent sequence is bounded. Deter- mine if the following statements are true or false, and if false, give a coun- terexample: (a) If (an) is bounded, then it converges. (b) If [an] is not bounded, then it diverges. (c) If (an) diverges, then it is not bounded. (a) an = √4+n 14. Suppose that lim an = 4 and lim bn = 7. Determine: 848 818 (a) lim (an + bn) 848 (c) lim cos(лbn) 818 17, bn = In Exercises 15-28, use Theorem 1 to determine the limit of the sequence or state that the sequence diverges. 13 oryang art nl 15) an = 5 - 2n 12581/1)-n drive (19. an = 252 21. Cn = 9n 23. an = 25. an In 27. Zn = 5n -1 12n +9 29, an= √n² +1 n 4+ 12n+2 -9+4n n (b) lim a 1148 screa mil straw 3 (d) lim (a-2anbn) 818 TH 18. an = 16. an 20- 20. Zn = n+1 en 28. yn = ne¹/n 900Sunga In Exercises 29-32, use Theorem 4 to determine the limit of the sequenc =e4n/(3n+9) 4 -n² 4+n-3n² 4n² +1 n (3) 10-1/n 22. Zn = 24. an = n √n³+1 26. rn = Inn - In(n² + 1) 30. an
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