Explanation Given information: The sequence a n = 3 n + 2 5 n Concept used: The sequence a n is convergent if L < 1 where L = lim n → ∞ ( a n + 1 a n ) Calculation: Consider the given sequence a n = 3 n + 2 5 n Now a n + 1 = 3 n + 3 5 n + 1 Then L = lim n → ∞ ( a n + 1 a n ) L = lim n → ∞ ( 3 n + 3 5 n + 1 3 n + 2 5 n ) L = lim n → ∞ 3 5 L = 3 5 Since the condition L < 1 satisfied given sequence is convergent

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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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 2.1, Problem 24E

To determine

The limit if the given sequence converges.

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Chapter 2.1, Problem 23E

Chapter 2.1, Problem 25E

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Chapter 2 Solutions

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Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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The limit if the given sequence converges.

Solution Summary: The author explains that the sequence a_n is convergent if L1 is satisfied.

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The limit if the given sequence converges.

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Chapter 2 Solutions