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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- -

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- -

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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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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