Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
Related questions
Question
Number 17 please
![1-8 ▪ Determine whether the sequence is convergent or diver-
gent. If it is convergent, find its limit.
1. dn =
3. an
5. an
n sin n
n' +1
7. {(1 + 3/n)4"}
8
9. Σ
11. Σ
00
13. Σ
8
15. Σ
2 +η
1 + 2n³
1 + n²
1
n=2 n v In n
17. Σ
9-20 » Determine whether the series is convergent or divergent.
* n’ + 1
n' + 1
18. Σ
cos 3n
n=11+ (1.2)"
η
n' + 1
20. Σ
n=1
1.3.5
(-5) ²n
n-1 n²9n
19. Σ (-1)-1 -
n=1
...
.. (2n-1)
5"n!
√n
n + 1
98+1
10"
4. an = cos(nπ/2)
Vn+ 1 - Vn-1
Η
2. απ
In n
√n
8. {(-10)"/n!}
6. din
10. Σ
1
(-1)"
12. Σ
ni_n + 1
M8 IM8 IM
n
In
14. Σ (31)
3η
n2n
n=1 (1 + 2n²)"
16. Σ
EXERCISES
21-24 = Determine whether the series is conditionally conver-
gent, absolutely convergent, or divergent.
21. Σ (-1)"-n-1/3
8
22. Σ (-1)"¯n-3
23. Σ
25-29 • Find the sum of the series.
2²n+1
Σ
25. Σ 5"
27.
(1)"(n + 1)3"
22+1
Σ [tan'(n + 1) – tan'n]
(-1)" 7"
-0 32" (2n)!
28. Σ
29. 1 - e t
el
3!
2!
33. Find the sum of the series Σ
Σ
Π
decimal places.
4!
34. (a) Show that the series
(b) Deduce that lim
818
30. Express the repeating decimal 4.173263
fraction.
31. Show that coshx > 1 + x? for all x.
32. For what values of x does the series Σ
0
36. Σ (−1)"
n?5"
Η
(2η)!
* Σ
-
24.
n"
n-1 (2n)!
0.
2
Σ
26. Σ -
n
(−1)²+¹
ης
35. Prove that if the series En-1 an is absolu
the series
is co
is also absolutely convergent.
36-39 • Find the radius of convergence ar
gence of the series.
00
37. Σ
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Transcribed Image Text:1-8 ▪ Determine whether the sequence is convergent or diver-
gent. If it is convergent, find its limit.
1. dn =
3. an
5. an
n sin n
n' +1
7. {(1 + 3/n)4"}
8
9. Σ
11. Σ
00
13. Σ
8
15. Σ
2 +η
1 + 2n³
1 + n²
1
n=2 n v In n
17. Σ
9-20 » Determine whether the series is convergent or divergent.
* n’ + 1
n' + 1
18. Σ
cos 3n
n=11+ (1.2)"
η
n' + 1
20. Σ
n=1
1.3.5
(-5) ²n
n-1 n²9n
19. Σ (-1)-1 -
n=1
...
.. (2n-1)
5"n!
√n
n + 1
98+1
10"
4. an = cos(nπ/2)
Vn+ 1 - Vn-1
Η
2. απ
In n
√n
8. {(-10)"/n!}
6. din
10. Σ
1
(-1)"
12. Σ
ni_n + 1
M8 IM8 IM
n
In
14. Σ (31)
3η
n2n
n=1 (1 + 2n²)"
16. Σ
EXERCISES
21-24 = Determine whether the series is conditionally conver-
gent, absolutely convergent, or divergent.
21. Σ (-1)"-n-1/3
8
22. Σ (-1)"¯n-3
23. Σ
25-29 • Find the sum of the series.
2²n+1
Σ
25. Σ 5"
27.
(1)"(n + 1)3"
22+1
Σ [tan'(n + 1) – tan'n]
(-1)" 7"
-0 32" (2n)!
28. Σ
29. 1 - e t
el
3!
2!
33. Find the sum of the series Σ
Σ
Π
decimal places.
4!
34. (a) Show that the series
(b) Deduce that lim
818
30. Express the repeating decimal 4.173263
fraction.
31. Show that coshx > 1 + x? for all x.
32. For what values of x does the series Σ
0
36. Σ (−1)"
n?5"
Η
(2η)!
* Σ
-
24.
n"
n-1 (2n)!
0.
2
Σ
26. Σ -
n
(−1)²+¹
ης
35. Prove that if the series En-1 an is absolu
the series
is co
is also absolutely convergent.
36-39 • Find the radius of convergence ar
gence of the series.
00
37. Σ
Unless otherwise noted, all content c
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