In exercises 1-40, determine whether the series is absolutely convergent, conditionally convergent or divergent. (-1)*. k! 2. km0 k=0 (-1 k-0 k 5. Σ (-1)* k2 + 1 1)k+1k² + 1 k 6. k=1 k=1 3* 7. Σ-: k! 10 (-1*. k! k=3

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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In exercises 1-40, determine whether the series is absolutely
convergent, conditionally convergent or divergent.
3
-1)*
6.
1)4
k-0
k0
E(-1)*2*
4.
(-1)
k-0
k-0
00
k
5. (-1)*+1
k² + 1
6. Č-1*+1k² + 1
(-1)*+1
k
k=1
k=1
7.
k=3
k!
k=4
k
(-1)*+
9.
10. Σ
4
2k + 1
(-1)*+1
k=2
k=3
2k + 1
k2*
k²3k
(-1
24
k=6
4k
13.
1– 3k
5k + 1
4k
15.
16.
k-l
17. Σ-
(-1)*+1.
km0
k
18. (-1)*+1
k³ + 1
k +1
k=2
k²
19. *
20. Σte
ek
k=7
k=1
2
k 3k
22.
sin k
23.
cos k
k3
k2
cos ka
25.
tan¬ k
k
26.
k
k=1
(-1)*
27.
(-1)*
28. 5
2 k In k
In k
(-1)*
(-1)*+1
30.
k=1
31. У
S 2k
32.
kk
k=3
E 34
k-8
33. Č(-1)*+1*!
34. (-1*+1k-4*
k!
k-6
4k
k4
(~1)k+1 k10
(2k)!
4k
36. (-1)*
k=1
(2k + 1)!
k=0
Transcribed Image Text:In exercises 1-40, determine whether the series is absolutely convergent, conditionally convergent or divergent. 3 -1)* 6. 1)4 k-0 k0 E(-1)*2* 4. (-1) k-0 k-0 00 k 5. (-1)*+1 k² + 1 6. Č-1*+1k² + 1 (-1)*+1 k k=1 k=1 7. k=3 k! k=4 k (-1)*+ 9. 10. Σ 4 2k + 1 (-1)*+1 k=2 k=3 2k + 1 k2* k²3k (-1 24 k=6 4k 13. 1– 3k 5k + 1 4k 15. 16. k-l 17. Σ- (-1)*+1. km0 k 18. (-1)*+1 k³ + 1 k +1 k=2 k² 19. * 20. Σte ek k=7 k=1 2 k 3k 22. sin k 23. cos k k3 k2 cos ka 25. tan¬ k k 26. k k=1 (-1)* 27. (-1)* 28. 5 2 k In k In k (-1)* (-1)*+1 30. k=1 31. У S 2k 32. kk k=3 E 34 k-8 33. Č(-1)*+1*! 34. (-1*+1k-4* k! k-6 4k k4 (~1)k+1 k10 (2k)! 4k 36. (-1)* k=1 (2k + 1)! k=0
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ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage