Explanation Definition used: “The sequence { a n } converges to L provided the terms of a n can be made arbitrarily close to L by taking n sufficiently large. That is, { a n } has the unique limit L if given any ε > 0 , it is possible to find a positive integer N (depending only on ε ) such that | a n − L | < ε whenever n > N , which can be expressed as lim n → ∞ a n = L .” Proof: Consider the sequence a n = 1 n 2 . Choose the positive integer N and given any ε > 0 . From the definition, there exist a real number n sufficiently large such that, | a n − 0 | < ε whenever n > N

Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)

2nd Edition

ISBN: 9780321965172

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

Publisher: PEARSON

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Limits

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Chapter 8.2, Problem 70E

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To prove: The limit of the sequence {1n2} is 0 using the formal definition of the limit of the sequence.

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Chapter 8.2, Problem 69E

Chapter 8.2, Problem 71E

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Chapter 8 Solutions

Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)

Ch. 8.1 - Prob. 1QC Ch. 8.1 - Prob. 2QC Ch. 8.1 - Prob. 3QC Ch. 8.1 - Prob. 4QC Ch. 8.1 - Prob. 5QC 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

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To prove: The limit of the sequence { 1 n 2 } is 0 using the formal definition of the limit of the sequence.

Solution Summary: The author explains that the limit of the sequence left1n2right is 0 using the formal definition.