Explanation Given: The telescoping series is ∑ k = 0 ∞ ( sin ( ( k + 1 ) π 2 k + 1 ) − sin ( k π 2 k − 1 ) ) . Calculation: Let s n be the n th partial sum of the series ∑ k = 0 ∞ ( sin ( ( k + 1 ) π 2 k + 1 ) − sin ( k π 2 k − 1 ) ) . Then, S n = ∑ k = 0 n ( sin ( ( k + 1 ) π 2 k + 1 ) − sin ( k π 2 k − 1 ) ) = { ( sin ( ( 1 + 1 ) π 2 + 1 ) − sin ( π 2 − 1 ) ) + ( sin ( ( 2 + 1 ) π 2 ( 2 ) + 1 ) − sin ( 2 π 2 ( 2 ) − 1 ) ) + ⋯ + ( sin ( ( n − 1 + 1 ) π 2 ( n − 1 ) + 1 ) − sin ( ( n − 1 ) π 2 ( n − 1 ) − 1 ) ) + ( sin ( ( n + 1 ) π 2 n + 1 ) − sin ( n π 2 n − 1 ) ) } = {

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Chapter 8.3, Problem 66E

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To find: The formula for the nth term of the sequence of partial sums {Sn} and then evaluate limn→∞Sn to obtain the value of the series or state that the series diverges.

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Chapter 8.3, Problem 65E

Chapter 8.3, Problem 67E

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Chapter 8 Solutions

Calculus: Early Transcendentals (2nd Edition)

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 formula for the n th term of the sequence of partial sums { S n } and then evaluate lim n → ∞ S n to obtain the value of the series or state that the series diverges.

Solution Summary: The author explains how to find the formula for the nth term of the sequence of partial sums leftS_nright and then evaluate it to obtain the series value or state that the

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To find: The formula for the nth term of the sequence of partial sums {Sn} and then evaluate limn→∞Sn to obtain the value of the series or state that the series diverges.

Want to see the full answer?

Chapter 8 Solutions