Explanation Given: ∑ n = 1 ∞ ( − 1 ) n n 3 + n Formula Used: The error bound for the alternating series is | S N − S | ≤ a N + 1 … ( 1 ) Calculation: Consider a n = ( − 1 ) n n 3 + n It can be observed that this is an alternating series, the value of which depends on the value of n . The value is positive for even values of n and negative for the odd values of n . The error bound for the alternating series is determined using the formula (1)...

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ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 11, Problem 60CRE

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The approximation of $\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n^{3} + \sqrt{n}}$ to within an error of at most $10^{- 5}$ using a computer algebra system.

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Chapter 11, Problem 59CRE

Chapter 11, Problem 61CRE

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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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The approximation of ∑ n = 1 ∞ ( − 1 ) n n 3 + n to within an error of at most 10 − 5 using a computer algebra system.

Solution Summary: The author calculates the error bound for the alternating series using a computer algebra system. The value is positive for even values and negative for odd values.

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To calculate:

The approximation of $\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n^{3} + \sqrt{n}}$ to within an error of at most $10^{- 5}$ using a computer algebra system.

Want to see the full answer?

Chapter 11 Solutions

The approximation of ∑ n = 1 ∞ ( − 1 ) n n 3 + n to within an error of at most 10 − 5 using a computer algebra system.

Solution Summary: The author calculates the error bound for the alternating series using a computer algebra system. The value is positive for even values and negative for odd values.

Concept explainers

Videos

To calculate: The approximation of ∑n=1∞(−1)nn3+n to within an error of at most 10−5 using a computer algebra system.

Want to see the full answer?

Chapter 11 Solutions

To calculate:

The approximation of $\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n^{3} + \sqrt{n}}$ to within an error of at most $10^{- 5}$ using a computer algebra system.