Explanation Given: b n = a n + 1 Calculation: Let { a n } converges to l and b n = a n + 1 And let ε > 0 Since, { a n } converges to l, by definition,, there is an M such that | a n − l | < ε for all n > M . Now, let N = M − 1 Therefore, we can say that whenever n > N , then n + 1 >&#...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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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 11.1, Problem 85E

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By using the limit definition that if ${a_{n}}$ converges then ${b_{n}}$ also converges and $\lim_{n \to \infty} a_{n} = \lim_{n \to \infty} b_{n}$

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Chapter 11.1, Problem 84E

Chapter 11.1, Problem 86E

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Chapter 11 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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By using the limit definition that if { a n } converges then { b n } also converges and lim n → ∞ a n = lim n → ∞ b n

Solution Summary: The author explains that if a n converges to l, there is an M such that when N > N, then N + 1 > M = M.

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By using the limit definition that if ${a_{n}}$ converges then ${b_{n}}$ also converges and $\lim_{n \to \infty} a_{n} = \lim_{n \to \infty} b_{n}$

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Chapter 11 Solutions

By using the limit definition that if { a n } converges then { b n } also converges and lim n → ∞ a n = lim n → ∞ b n

Solution Summary: The author explains that if a n converges to l, there is an M such that when N > N, then N + 1 > M = M.

Concept explainers

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By using the limit definition that if {an} converges then {bn} also converges and limn→∞an=limn→∞bn

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Chapter 11 Solutions

By using the limit definition that if ${a_{n}}$ converges then ${b_{n}}$ also converges and $\lim_{n \to \infty} a_{n} = \lim_{n \to \infty} b_{n}$