Explanation Concept Used: Divergence Test states that if lim k → ∞ a k ≠ 0 then ∑ a k will diverge. The given series is ∑ a k = ∑ k = 1 ∞ k ! k 2 ( k + 1 ) 2 ⇒ a k = k ! k 2 ( k + 1 ) 2 Observe that: lim k → ∞ a k = lim k → ∞ k ! k 2 ( k + 1 ) 2 = lim k → ∞ k ( k − 1 ) ( k − 2

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 8, Problem 41SP

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To find: if the given series converges or diverges. ∑k=1∞k!k2 (k+1)2 .

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Chapter 8, Problem 40SP

Chapter 8, Problem 42SP

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Problem 6. Does the series 2n2 converge? (Hint: n! < n".) n! n=0

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12) There is one special “family” of series for which, if the series converges, we can determine the exact value of the series. This is the family where it really matters that we know the bounds of the summation. What family is this?

Chapter 8 Solutions

Calculus

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if the given series converges or diverges. ∑ k = 1 ∞ k ! k 2 ( k + 1 ) 2 .

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To find: if the given series converges or diverges. ∑k=1∞k!k2 (k+1)2 .

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Chapter 8 Solutions