Explanation Given: π − π 3 3 ! + π 5 5 ! − π 7 7 ! + ... , Calculation: Step 1: Set x = π in the Maclaurin series for sin x to obtain: 0 = sin π = π − π 3 3 ! + π 5 5 ! − π 7 7 ! + ... Step 2: Using the error bound for an alternating series, we have | 0 − ∑ n = 0 N ( − 1 ) n π 2 n +

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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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 11.7, Problem 46E

To determine

That $π - \frac{π^{3}}{3!} + \frac{π^{5}}{5!} - \frac{π^{7}}{7!} + ...$ converges to zero and the number of terms that must be computed to get within 0.01 of zero?

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Chapter 11.7, Problem 45E

Chapter 11.7, Problem 47E

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Chapter 11 Solutions

Calculus - Standalone book

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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That π − π 3 3 ! + π 5 5 ! − π 7 7 ! + ... converges to zero and the number of terms that must be computed to get within 0.01 of zero?

Solution Summary: The author explains that N = 4 is the smallest value for which the error bound is less than 0.01, so five terms are needed.

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That $π - \frac{π^{3}}{3!} + \frac{π^{5}}{5!} - \frac{π^{7}}{7!} + ...$ converges to zero and the number of terms that must be computed to get within 0.01 of zero?

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Chapter 11 Solutions

That π − π 3 3 ! + π 5 5 ! − π 7 7 ! + ... converges to zero and the number of terms that must be computed to get within 0.01 of zero?

Solution Summary: The author explains that N = 4 is the smallest value for which the error bound is less than 0.01, so five terms are needed.

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That π−π33!+π55!−π77!+... converges to zero and the number of terms that must be computed to get within 0.01 of zero?

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Chapter 11 Solutions

That $π - \frac{π^{3}}{3!} + \frac{π^{5}}{5!} - \frac{π^{7}}{7!} + ...$ converges to zero and the number of terms that must be computed to get within 0.01 of zero?