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 } = { n n } Observe that: { a n } = { n n } a 1 = 1 a 2 = 2 ≈ 1.414 a 3 = 3 3 ≈ 1.442 a 4 = 4 4 ≈ 1.414 a 5 = 5 5 = 1.379 ... etc Thus the sequence is a decreasing sequence

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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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 8.1, Problem 41PS

To determine

To show: the given sequence converges. {nn}

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Chapter 8.1, Problem 40PS

Chapter 8.1, Problem 42PS

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Chapter 8 Solutions

Student's Solution and Survival Manual for Calculus

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the given sequence converges. { n 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. {nn}

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Chapter 8 Solutions