Explanation Given: Given sequence ln 1 ln 2 , ln 2 ln 3 , ln 3 ln 4 , ln 4 ln 5 , ln 5 ln 6 , ln 6 ln 7 ........ Concept Used: A sequence { a n } is said to be convergent if the n t h term of the sequence approaches unique finite as n approaches ∞ otherwise sequence said to be divergent. Calculation: As we have ln 1 ln 2 , ln 2 ln 3 , ln 3 ln 4 , ln 4 ln 5 , ln 5 ln 6 , ln 6 ln 7 ........ , whose n t h term is { a n } = ln n ln n + 1 To evaluate limit of { a n } = ln n ln n + 1 as n → ∞ . lim n → ∞ { a n } = lim n → ∞ ln n ln n + 1 ( ∵ ∞ ∞ f o r m ) = lim n → ∞

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 3.6, Problem 2TF

To determine

Whether the given sequence ln1ln2,ln2ln3,ln3ln4,ln4ln5,ln5ln6,ln6ln7........ is convergent or divergent.

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Chapter 3.6, Problem 1TF

Chapter 3.6, Problem 3TF

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Chapter 3 Solutions

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Whether the given sequence ln 1 ln 2 , ln 2 ln 3 , ln 3 ln 4 , ln 4 ln 5 , ln 5 ln 6 , ln 6 ln 7 ........ is convergent or divergent.

Solution Summary: The author analyzes whether a given sequence mathrmln1mathria2 is convergent or divergent.

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Whether the given sequence ln1ln2,ln2ln3,ln3ln4,ln4ln5,ln5ln6,ln6ln7........ is convergent or divergent.

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Chapter 3 Solutions