Explanation Given: ∑ k = 1 ∞ b k = 0.54 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 sum of the given series ∑ k = 0 ∞ b k − 3 − k 2 can be calculated as shown: ∑ k = 0 ∞ b k − 3 − k 2 = 1 2 ∑ k = 0 ∞

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 8.2, Problem 40PS

To determine

To find: the value of the series: ∑k=0∞bk−3 −k2 given ∑k=1∞bk=0.54

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Chapter 8.2, Problem 39PS

Chapter 8.2, Problem 41PS

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Chapter 8 Solutions

Calculus

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the value of the series: ∑ k = 0 ∞ b k − 3 − k 2 given ∑ k = 1 ∞ b k = 0.54

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 value of the series: ∑k=0∞bk−3 −k2 given ∑k=1∞bk=0.54

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Chapter 8 Solutions