a. Explanation Explanation Given: The infinite series is ∑ k = 1 ∞ ( 1 2 k − 1 2 k + 1 ) . Calculation: Let s n be the n th partial sum of the series ∑ k = 1 ∞ ( 1 2 k − 1 2 k + 1 ) . Then, s n = ∑ k = 1 n ( 1 2 k − 1 2 k + 1 ) = ( 1 2 1 − 1 2 1 + 1 ) + ( 1 2 2 − 1 2 2 + 1 ) + ⋯ + ( 1 2 n − 1 − 1 2 n − 1 + 1 ) + ( 1 2 n − 1 2 n + 1 ) = ( 1 2 1 − 1 2 2 ) + ( 1 2 2 − 1 2 3 ) + ⋯ + ( 1 2 n − 1 − 1 2 n ) + ( 1 2 n − 1 2 n + 1 ) Here, it is noticed that the terms are cancelled (telescoping sum) except the first term of the first parentheses and the second term of the last parentheses b. To determine To evaluate: The series by a geometric series argument.

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 8.3, Problem 74E

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To evaluate: The series by a telescopic series argument.

To determine

To evaluate: The series by a geometric series argument.

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Chapter 8.3, Problem 73E

Chapter 8.3, Problem 75E

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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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The series by a telescopic series argument.

Solution Summary: The author evaluates the infinite series by a telescopic series argument.

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Chapter 8 Solutions