80 =Consider the series Σ where p is a real number. 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. a. Integrate f(x). 00 1 1 dx= lim ( x(In x) b→∞ Evaluate and simplify. p-1 lim 1 k=2 k(Ink)P b- 0040 For what values of p does the series converge? The series converges for p b. Does this series converge faster for p = 2 or p=3? OA. The series converges faster for p = 3 because the denominator of the expression gets larger faster. OB. The series converges faster for p = 2 because the denominator of the expression gets smaller faster. OC. The series converges faster for p = 3 because the denominator of the expression gets smaller faster. OD. The series converges faster for p = 2 because the denominator of the expression gets larger faster.
80 =Consider the series Σ where p is a real number. 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. a. Integrate f(x). 00 1 1 dx= lim ( x(In x) b→∞ Evaluate and simplify. p-1 lim 1 k=2 k(Ink)P b- 0040 For what values of p does the series converge? The series converges for p b. Does this series converge faster for p = 2 or p=3? OA. The series converges faster for p = 3 because the denominator of the expression gets larger faster. OB. The series converges faster for p = 2 because the denominator of the expression gets smaller faster. OC. The series converges faster for p = 3 because the denominator of the expression gets smaller faster. OD. The series converges faster for p = 2 because the denominator of the expression gets larger faster.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the series Σ
, where p is a real number.
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.
a. Integrate f(x).
∞0
2
1
x(Inx)P
1
1
k=2 k(Ink)P
Evaluate and simplify.
p-
dx = lim 12
b-8
lim
b→∞
For what values of p does the series converge?
The series converges for p ▼
b. Does this series converge faster for p = 2 or p = 3?
←
OA. The series converges faster for p = 3 because the denominator of the expression gets larger faster.
OB. The series converges faster for p = 2 because the denominator of the expression gets smaller faster.
OC. The series converges faster for p = 3 because the denominator of the expression gets smaller faster.
OD. The series converges faster for p = 2 because the denominator of the expression gets larger faster.
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