Explanation If a convergent sequence has increasing terms then the limit will be called the upper limit of the sequence and if a convergent sequence has decreasing terms then the limit will be called the lower limit of the sequence. The given sequence is { a n } = { ln ( n + 1 n ) } Observe that: { a n } = { ln ( n + 1 n ) } a 1 = ln ( 2 ) a 2 = ln ( 3 2 ) a 3 = ln ( 4 3 ) a 4 = ln ( 5 4 )

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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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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Question

Chapter 8.1, Problem 37PS

To determine

To show: the given sequence converges. {ln(n+1n)}

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Chapter 8.1, Problem 36PS

Chapter 8.1, Problem 38PS

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Chapter 8 Solutions

Calculus

Ch. 8.1 - Prob. 1PS Ch. 8.1 - Prob. 2PS Ch. 8.1 - Prob. 3PS Ch. 8.1 - Prob. 4PS Ch. 8.1 - Prob. 5PS Ch. 8.1 - Prob. 6PS Ch. 8.1 - Prob. 7PS Ch. 8.1 - Prob. 8PS Ch. 8.1 - Prob. 9PS Ch. 8.1 - Prob. 10PS

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the given sequence converges. { ln ( n + 1 n ) }

Solution Summary: The author explains that if a convergent sequence has increasing terms then the limit will be called the upper limit of the sequence.

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To show: the given sequence converges. {ln(n+1n)}

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Chapter 8 Solutions