Explanation Given: The value of the series ∑ a k is A and ∑ b k is B. Proof: ∑ k = 1 ∞ ( a k ± b k ) = lim n → ∞ ∑ k = 1 n ( a k ± b k ) [ Definition of infinite series ] = lim n → ∞ [ ∑ k = 1 n a k ± ∑ k = 1 n b k ] x

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

2nd Edition

ISBN: 9780321954329

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

Publisher: PEARSON

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Chapter 8.4, Problem 62E

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To prove: If the series ∑ak converges to A and ∑bk converges to B, then ∑k=1∞(ak±bk)=A+B”using in the proof property 1 of Theorem 8.13.

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Chapter 8.4, Problem 61E

Chapter 8.4, Problem 63E

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Chapter 8 Solutions

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

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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To prove: If the series ∑ a k converges to A and ∑ b k converges to B , then ∑ k = 1 ∞ ( a k ± b k ) = A + B ”using in the proof property 1 of Theorem 8.13.

Solution Summary: The author explains the proof property 1 of Theorem 8.13.

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To prove: If the series ∑ak converges to A and ∑bk converges to B, then ∑k=1∞(ak±bk)=A+B”using in the proof property 1 of Theorem 8.13.

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Chapter 8 Solutions