Explanation Given: ∑ k = 0 ∞ [ ( 2 3 ) k + ( 3 4 ) k ] 2 Concept Used: Geometric Series A geometric series is any series that can be written in the form, ∑ n = 1 ∞ a r n − 1 or ∑ n = 0 ∞ a r n Geometric series will converge if − 1 < r < 1 and its sum is given by, ∑ n = 1 ∞ a r n − 1 = ∑ n = 0 ∞ a r n = a 1 − r The given series is ∑ a k = ∑ k = 0 ∞ [ ( 2 3 ) k + ( 3 4 ) k ] 2 = ∑ k = 0 ∞ [ ( 2 3 ) 2 k + ( 3 4 ) 2 k + 2 ( 2 3 ) k (

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 8.2, Problem 42PS

To determine

To find: the sum of the given convergent series ∑k=0∞[ ( 2 3 ) k+ ( 3 4 ) k]2 .

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Chapter 8.2, Problem 41PS

Chapter 8.2, Problem 43PS

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Chapter 8 Solutions

Calculus

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the sum of the given convergent series ∑ k = 0 ∞ [ ( 2 3 ) k + ( 3 4 ) k ] 2 .

Solution Summary: The author explains that a geometric series is any series that can be written in the form of -1r1 and its sum is given by.

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To find: the sum of the given convergent series ∑k=0∞[ ( 2 3 ) k+ ( 3 4 ) k]2 .

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Chapter 8 Solutions