Explanation Given: Given series ∑ k = 1 ∞ ( − 1 ) k + 1 k 2 k 2 + 1 Concept Used: An alternating series ∑ ( − 1 ) k a k with a k > 0 converges if a k + 1 ≤ a k for k = 1 , 2 , 3...... and lim k → 0 a k = 0. A series ∑ ( − 1 ) k a k is said to be absolute convergent if both ∑ ( − 1 ) k a k and ∑ | a k | converges together whereas ∑ ( − 1 ) k a k is said to be conditional convergent if ∑ ( − 1 ) k a k convergent but ∑ | a k | divergent

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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Chapter 8.6, Problem 6PS

To determine

Whether the given series ∑k=1∞ ( −1 ) k+1k2k2+1 is converges absolutely, converges conditionally or diverges.

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Chapter 8.6, Problem 5PS

Chapter 8.6, Problem 7PS

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Chapter 8 Solutions

Student's Solution and Survival Manual for Calculus

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Whether the given series ∑ k = 1 ∞ ( − 1 ) k + 1 k 2 k 2 + 1 is converges absolutely, converges conditionally or diverges.

Solution Summary: The author analyzes whether the given series displaystyle 'underset' is convergent, conditionally, or diverges.

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Whether the given series ∑k=1∞ ( −1 ) k+1k2k2+1 is converges absolutely, converges conditionally or diverges.

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Chapter 8 Solutions