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 = b − n . 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 . That is, | b − n − 0 | < ε whenever n > N . Solve and obtain the value of n

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ISBN: 9781323178522

Author: Briggs

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 72E

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To prove: The limit of the sequence {b−n} is 0 for b>1 using the formal definition of the limit of the sequence.

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Chapter 8.2, Problem 71E

Chapter 8.2, Problem 73E

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To prove: The limit of the sequence { b − n } is 0 for b > 1 using the formal definition of the limit of the sequence.

Solution Summary: The author explains that the limit of the sequence leftb-nright is 0 for b>1.

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To prove: The limit of the sequence {b−n} is 0 for b>1 using the formal definition of the limit of the sequence.

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Chapter 8 Solutions

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To prove: The limit of the sequence { b − n } is 0 for b &gt; 1 using the formal definition of the limit of the sequence.

Solution Summary: The author explains that the limit of the sequence leftb-nright is 0 for b>1.

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To prove: The limit of the sequence {b−n} is 0 for b>1 using the formal definition of the limit of the sequence.

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Chapter 8 Solutions

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To prove: The limit of the sequence { b − n } is 0 for b > 1 using the formal definition of the limit of the sequence.