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(-1)n-1

(-1)n-1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Determine whether the series is absolutely convergent, conditionally convergent, or divergent (In your written solution, be sure to show all work and justify all steps.): 

 

Certainly! Below is the transcription of the image for an educational website: --- ### Summation Series The given mathematical expression is a summation series, which is defined as follows: \[ \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n+8} \] #### Explanation: - The symbol \(\sum\) (sigma) represents the summation notation. - The variable \(n\) is the index of summation, starting from \(n=1\). - \(\infty\) indicates that the summation extends to infinity. - The term \(\frac{(-1)^{n-1}}{n+8}\) is the general term of the series. In this series: - \((-1)^{n-1}\) alternates the sign of each term (positive when \(n\) is odd and negative when \(n\) is even). - \(n+8\) appears in the denominator. This series is a fascinating example of an alternating series that involves both positive and negative fractions. --- This detailed explanation helps students or readers understand the components and structure of the given mathematical summation.
Transcribed Image Text:Certainly! Below is the transcription of the image for an educational website: --- ### Summation Series The given mathematical expression is a summation series, which is defined as follows: \[ \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n+8} \] #### Explanation: - The symbol \(\sum\) (sigma) represents the summation notation. - The variable \(n\) is the index of summation, starting from \(n=1\). - \(\infty\) indicates that the summation extends to infinity. - The term \(\frac{(-1)^{n-1}}{n+8}\) is the general term of the series. In this series: - \((-1)^{n-1}\) alternates the sign of each term (positive when \(n\) is odd and negative when \(n\) is even). - \(n+8\) appears in the denominator. This series is a fascinating example of an alternating series that involves both positive and negative fractions. --- This detailed explanation helps students or readers understand the components and structure of the given mathematical summation.
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