Explanation Definition used: Limit of a Sequence : Let { a n } be a sequence. If the sequence { a n } is said to be convergent then the limit L can be written as lim n → ∞ a n = L , if the terms of the sequence, a n , can be made as close to L by taking n sufficiently large. If a sequence is not convergent, it is said to be divergent. Calculation: The given sequence is { a n } = { n n 2 + 1 } The functional values of f ( n ) = n n 2 + 1 for n = 1 , 2 , 3 , 4 , 5 ⋯ Substitute n = 1 in f ( n ) = n n 2 + 1 . f ( 1 ) = 1 1 2 + 1 = 1 2 = 0.5 Substitute n = 2 in f ( n ) = n n 2 + 1 . f ( 2 ) = 2 2 2 + 1 = 2 4 + 1 = 2 5 = 0.4 Substitute n = 3 in f ( n ) = n n 2 + 1 . f ( 3 ) = 3 3 2 + 1 = 3 9 + 1 = 3 10 = 0.3 Substitute n = 4 in f ( n ) = n n 2 + 1 . f ( 4 ) = 4 4 2 + 1 = 4 16 + 1 = 4 17 = 0

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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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 11.2, Problem 30E

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Whether the sequence {an}={nn2+1} converges or diverges; find its limit if the sequence converges.

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Chapter 11.2, Problem 29E

Chapter 11.2, Problem 31E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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Whether the sequence { a n } = { n n 2 + 1 } converges or diverges; find its limit if the sequence converges.

Solution Summary: The author explains that if the sequence lefta_nright is convergent, it is said to be divergent.

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Whether the sequence {an}={nn2+1} converges or diverges; find its limit if the sequence converges.

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Chapter 11 Solutions