Explanation Given: The sequence is a n = 75 n − 1 99 n + 5 n sin n 8 n . Theorem used: Squeeze Theorem : (1) If x n ≤ z n ≤ y n for n ≥ N and lim n → ∞ x n = lim n → ∞ y n = L , then the value of lim n → ∞ z n is L . (2) The sequence { r n } converges to zero when − 1 < r < 1 . That is, lim n → ∞ r n = 0 if − 1 < r < 1 . Calculation: Compute, lim n → ∞ a n = lim n → ∞ 75 n − 1 99 n + lim n → ∞ 5 n sin n 8 n (1) Find the limit of the sequence { 75 n − 1 99 n } . lim n → ∞ a n = lim n → ∞ ( 75 n − 1 99 n ) = lim n → ∞ 1 75 ⋅ ( 75 99 ) n = 1 75 lim n → ∞ ( 75 99 ) n Since 75 99 < 1 , the value of lim n → ∞ ( 75 n − 1 99 n ) = 0

Calculus: Early Transcendentals, 2nd Edition

2nd Edition

ISBN: 9780321965165

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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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 8.2, Problem 79E

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To evaluate: The limit of the given sequence or state why the limit does not exist for the sequence an=75n−199n+5nsinn8n.

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Chapter 8.2, Problem 78E

Chapter 8.2, Problem 80E

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Chapter 8 Solutions

Calculus: Early Transcendentals, 2nd Edition

Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

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The limit of the given sequence or state why the limit does not exist for the sequence a n = 75 n − 1 99 n + 5 n sin n 8 n .

Solution Summary: The author evaluates the sequence's limit or states why the limit doesn't exist.

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To evaluate: The limit of the given sequence or state why the limit does not exist for the sequence an=75n−199n+5nsinn8n.

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Chapter 8 Solutions