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Math
CalculusCalculus10th Edition

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Chapter 9.2, Problem 103E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
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Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
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Problem 13E
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Problem 15E
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Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
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Problem 26E
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Problem 37E
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Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
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Problem 53E
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Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
Problem 84E
Problem 85E
Problem 86E
Problem 87E
Problem 88E
Problem 89E
Problem 90E
Problem 91E
Problem 92E
Problem 93E
Problem 94E
Problem 95E
Problem 96E
Problem 97E
Problem 98E
Problem 99E
Problem 100E
Problem 101E
Problem 102E
Problem 103E
Problem 104E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Express ∑ k = 1 ∞ 6 k ( 3 k + 1 − 2 k + 1 ) ( 3 k − 2 k ) as a rational number.

To determine

To Calculate: The expression ∑k=1∞6k(3k+1−2k+1)(3k−2k) as a rational number[p/q form].

Explanation

Given:∑k=1∞6k(3k+1−2k+1)(3k−2k)

Calculation:

∑k=1∞6k(3k+1−2k+1)(3k−2k)

=∑k=1∞(2.3)k(3k+1−2k+1)(3k−2k)

=∑k=1∞2k3k(3k+1−2k+1)(3k−2k)

=∑k=1∞2k3k(3−2)(3k+1−2k+1)(3k−2k)

=∑k=1∞2k3k(3)−2k3k(2)(3k+1−2k+1)(3k−2k)

By adding and subtracting 3k3k+1 from the numerator, we get

=∑k=1∞2k3k(3)−2k3k(2)+3k

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Chapter 9.2,
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Sect-9.1 P-1ESect-9.1 P-2ESect-9.1 P-3ESect-9.1 P-4ESect-9.1 P-5ESect-9.1 P-6ESect-9.1 P-7ESect-9.1 P-8ESect-9.1 P-9ESect-9.1 P-10E
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P-41ESect-9.7 P-42ESect-9.7 P-43ESect-9.7 P-44ESect-9.7 P-45ESect-9.7 P-46ESect-9.7 P-47ESect-9.7 P-49ESect-9.7 P-48ESect-9.7 P-50ESect-9.7 P-51ESect-9.7 P-52ESect-9.7 P-53ESect-9.7 P-54ESect-9.7 P-55ESect-9.7 P-56ESect-9.7 P-57ESect-9.7 P-58ESect-9.7 P-60ESect-9.7 P-61ESect-9.7 P-64ESect-9.7 P-65ESect-9.7 P-66ESect-9.7 P-67ESect-9.7 P-68ESect-9.7 P-69ESect-9.7 P-70ESect-9.7 P-71ESect-9.8 P-1ESect-9.8 P-2ESect-9.8 P-3ESect-9.8 P-4ESect-9.8 P-5ESect-9.8 P-6ESect-9.8 P-7ESect-9.8 P-8ESect-9.8 P-9ESect-9.8 P-10ESect-9.8 P-11ESect-9.8 P-12ESect-9.8 P-13ESect-9.8 P-14ESect-9.8 P-15ESect-9.8 P-16ESect-9.8 P-17ESect-9.8 P-18ESect-9.8 P-19ESect-9.8 P-20ESect-9.8 P-21ESect-9.8 P-22ESect-9.8 P-23ESect-9.8 P-24ESect-9.8 P-25ESect-9.8 P-26ESect-9.8 P-27ESect-9.8 P-28ESect-9.8 P-29ESect-9.8 P-30ESect-9.8 P-31ESect-9.8 P-32ESect-9.8 P-33ESect-9.8 P-34ESect-9.8 P-35ESect-9.8 P-36ESect-9.8 P-37ESect-9.8 P-38ESect-9.8 P-39ESect-9.8 P-40ESect-9.8 P-41ESect-9.8 P-42ESect-9.8 P-43ESect-9.8 P-44ESect-9.8 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P-36ESect-9.9 P-37ESect-9.9 P-38ESect-9.9 P-39ESect-9.9 P-40ESect-9.9 P-41ESect-9.9 P-42ESect-9.9 P-43ESect-9.9 P-44ESect-9.9 P-45ESect-9.9 P-46ESect-9.9 P-47ESect-9.9 P-48ESect-9.9 P-49ESect-9.9 P-50ESect-9.9 P-51ESect-9.9 P-52ESect-9.9 P-53ESect-9.9 P-54ESect-9.9 P-55ESect-9.9 P-56ESect-9.9 P-57ESect-9.9 P-58ESect-9.9 P-59ESect-9.9 P-60ESect-9.9 P-61ESect-9.9 P-62ESect-9.10 P-81ESect-9.10 P-1ESect-9.10 P-2ESect-9.10 P-3ESect-9.10 P-4ESect-9.10 P-5ESect-9.10 P-6ESect-9.10 P-7ESect-9.10 P-8ESect-9.10 P-9ESect-9.10 P-10ESect-9.10 P-11ESect-9.10 P-12ESect-9.10 P-13ESect-9.10 P-14ESect-9.10 P-15ESect-9.10 P-16ESect-9.10 P-19ESect-9.10 P-17ESect-9.10 P-18ESect-9.10 P-20ESect-9.10 P-21ESect-9.10 P-22ESect-9.10 P-23ESect-9.10 P-24ESect-9.10 P-25ESect-9.10 P-26ESect-9.10 P-27ESect-9.10 P-28ESect-9.10 P-29ESect-9.10 P-30ESect-9.10 P-31ESect-9.10 P-32ESect-9.10 P-33ESect-9.10 P-34ESect-9.10 P-35ESect-9.10 P-36ESect-9.10 P-37ESect-9.10 P-38ESect-9.10 P-39ESect-9.10 P-40ESect-9.10 P-45ESect-9.10 P-46ESect-9.10 P-41ESect-9.10 P-42ESect-9.10 P-43ESect-9.10 P-44ESect-9.10 P-47ESect-9.10 P-48ESect-9.10 P-49ESect-9.10 P-50ESect-9.10 P-51ESect-9.10 P-52ESect-9.10 P-53ESect-9.10 P-54ESect-9.10 P-55ESect-9.10 P-56ESect-9.10 P-57ESect-9.10 P-58ESect-9.10 P-59ESect-9.10 P-60ESect-9.10 P-61ESect-9.10 P-62ESect-9.10 P-63ESect-9.10 P-64ESect-9.10 P-65ESect-9.10 P-66ESect-9.10 P-67ESect-9.10 P-68ESect-9.10 P-69ESect-9.10 P-70ESect-9.10 P-71ESect-9.10 P-72ESect-9.10 P-73ESect-9.10 P-74ESect-9.10 P-75ESect-9.10 P-76ESect-9.10 P-77ESect-9.10 P-78ESect-9.10 P-79ESect-9.10 P-80ESect-9.10 P-82ESect-9.10 P-83ESect-9.10 P-84ESect-9.10 P-85ESect-9.10 P-86ESect-9.10 P-87ESect-9.10 P-88ESect-9.10 P-89ESect-9.10 P-90ESect-9.10 P-91ESect-9.10 P-92ESect-9.10 P-93ESect-9.10 P-94ESect-9.10 P-95ESect-9.10 P-96ECh-9 P-1RECh-9 P-2RECh-9 P-3RECh-9 P-4RECh-9 P-5RECh-9 P-6RECh-9 P-7RECh-9 P-8RECh-9 P-9RECh-9 P-10RECh-9 P-14RECh-9 P-11RECh-9 P-15RECh-9 P-13RECh-9 P-12RECh-9 P-16RECh-9 P-17RECh-9 P-18RECh-9 P-19RECh-9 P-20RECh-9 P-21RECh-9 P-22RECh-9 P-23RECh-9 P-24RECh-9 P-25RECh-9 P-26RECh-9 P-27RECh-9 P-28RECh-9 P-29RECh-9 P-30RECh-9 P-31RECh-9 P-32RECh-9 P-33RECh-9 P-34RECh-9 P-35RECh-9 P-36RECh-9 P-37RECh-9 P-38RECh-9 P-40RECh-9 P-39RECh-9 P-41RECh-9 P-42RECh-9 P-43RECh-9 P-44RECh-9 P-45RECh-9 P-46RECh-9 P-47RECh-9 P-48RECh-9 P-49RECh-9 P-50RECh-9 P-51RECh-9 P-52RECh-9 P-53RECh-9 P-54RECh-9 P-55RECh-9 P-56RECh-9 P-57RECh-9 P-58RECh-9 P-59RECh-9 P-60RECh-9 P-61RECh-9 P-62RECh-9 P-65RECh-9 P-63RECh-9 P-64RECh-9 P-66RECh-9 P-67RECh-9 P-68RECh-9 P-69RECh-9 P-70RECh-9 P-72RECh-9 P-71RECh-9 P-73RECh-9 P-74RECh-9 P-75RECh-9 P-76RECh-9 P-77RECh-9 P-78RECh-9 P-79RECh-9 P-80RECh-9 P-81RECh-9 P-82RECh-9 P-83RECh-9 P-84RECh-9 P-85RECh-9 P-86RECh-9 P-87RECh-9 P-88RECh-9 P-89RECh-9 P-90RECh-9 P-91RECh-9 P-92RECh-9 P-93RECh-9 P-94RECh-9 P-95RECh-9 P-96RECh-9 P-97RECh-9 P-98RECh-9 P-99RECh-9 P-100RECh-9 P-101RECh-9 P-102RECh-9 P-103RECh-9 P-104RECh-9 P-105RECh-9 P-106RECh-9 P-107RECh-9 P-108RECh-9 P-109RECh-9 P-110RECh-9 P-1PSCh-9 P-2PSCh-9 P-3PSCh-9 P-4PSCh-9 P-5PSCh-9 P-6PSCh-9 P-7PSCh-9 P-8PSCh-9 P-9PSCh-9 P-10PSCh-9 P-11PSCh-9 P-12PSCh-9 P-13PSCh-9 P-14PSCh-9 P-15PSCh-9 P-16PS

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