Explanation Concept Used: Ratio Test: Let ∑ k = 1 ∞ a k be a series with nonzero terms. Let ρ = lim k → ∞ | a k + 1 a k | i. If ρ < 1 , then the series converges absolutely. ii. If ρ > 1 or ρ = ∞ , then the series diverges. iii. If ρ = 1 , the test does not provide any information. Given the power series ∑ k = 1 ∞ k ( 2 k − 1 ) ! , we start by applying ratio test to find if this series is convergent or not. In this case ∑ k = 1 ∞ a k = ∑ k = 1 ∞ k ( 2 k − 1 ) ! ⇒ a k = k ( 2 k − 1 ) ! Therefore, ρ = lim k → ∞ | a k + 1 a k | =

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 8, Problem 33SP

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To find: whether the given series converges or not. ∑k=1∞k(2k−1)! .

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Chapter 8, Problem 32SP

Chapter 8, Problem 34SP

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Chapter 8 Solutions

Calculus

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whether the given series converges or not. ∑ k = 1 ∞ k ( 2 k − 1 ) ! .

Solution Summary: The author explains how to find whether the given series is convergent or not.

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To find: whether the given series converges or not. ∑k=1∞k(2k−1)! .

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Chapter 8 Solutions