52-57. Choose your test Determine whether the following series con- verge or diverge. 52. 8 54. Σ k=0 k + 1 k 10 k² + 9 53. Ο 1 k= (3k + 1)(3k + 4) k ένα k=0 k² + 1 55. Σ α
52-57. Choose your test Determine whether the following series con- verge or diverge. 52. 8 54. Σ k=0 k + 1 k 10 k² + 9 53. Ο 1 k= (3k + 1)(3k + 4) k ένα k=0 k² + 1 55. Σ α
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
help with 55, explain how to do divergence test then perform otehr test to determine the convergence and divergence of this series?
Transcribed Image Text:or why not Determine whether the following state-
ments are true and give an explanation or counterexample.
a. If Σa, converges, then Σ ak converges.
k=
k=10
b. If Σakdiverges, then Σ ak diverges.
k=1
k=10
c. If a converges, then Σ(ak + 0.0001) also converges.
d. If Ep diverges, then Σ(p + 0.001)* diverges, for a fixed
real number p.
If Ek converges, then Σk-P+0.001 converges.
e.
f. If lim ak = 0, then Zak converges.
kis
52-57. Choose your test Determine whether the following series con-
verge or diverge.
52. Σ
54.
IM8 IM
56. Σ
k + 1
k
10
k² +9
2k + 3k
4k
53.
55.
57.
58. Log p-series Consider the series
number.
12
1
Σ
Σ
k=1 (3k + 1)(3k + 4)
8
Σ
k=0
or
k
√₁² + 1
1
k=2 k(ln k)p'
59. Loglog p-series Consider the series
is a real number.
∞4
Σ
{₂k1
k=2 k ln² k
a. Use the Integral Test to determine the values of p for which
this series converges.
b. Does this series converge faster for p = 2 or p = 3? Explain.
where p is a real
1
k=3 k ln k(In ln k)p³
a. For what values of p does this series converge?
b. Which of the following series converges faster? Explain.
1
where p
1
Σ
2k In k(In Ink)²
65.
66
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