Explanation Recall the property of limit; If lim n → ∞ a n = A and lim n → ∞ b n = B , then lim n → ∞ ( a n + b n ) = lim n → ∞ a n + lim n → ∞ b n = A + B . Consider the following example which will disprove the given statement. Let a n = ( − 1 ) n + 1 and b n = ( − 1 ) n . Suppose { a n } and { b n } are sequences. Find lim n → ∞ ( a n + b n ) . lim n → ∞ ( a n + b n ) = lim n → ∞ ( ( − 1 ) n + 1 + ( − 1 ) n ) = lim n → ∞ ( − ( − 1 ) n + ( − 1 ) n ) = lim n → ∞ ( 0 ) = 0 Now find lim n → ∞ a n

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 50E

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Whether the statement “If {an} and {bn} are sequences such that limn→∞(an+bn) exists, then both limn→∞an and limn→∞bn must exist” is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

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Chapter 11.2, Problem 49E

Chapter 11.2, Problem 51E

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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 statement “If { a n } and { b n } are sequences such that lim n → ∞ ( a n + b n ) exists, then both lim n → ∞ a n and lim n → ∞ b n must exist” is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

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Whether the statement “If {an} and {bn} are sequences such that limn→∞(an+bn) exists, then both limn→∞an and limn→∞bn must exist” is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

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Chapter 11 Solutions