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What is the value of E 4 7in-1 ? n- 1 Your answer:

What is the value of E 4 7in-1 ? n- 1 Your answer:

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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### Infinite Series Summation Problem **Question:** What is the value of \(\sum_{n=1}^{\infty} 4 \left(\frac{7}{6}\right)^{n-1}\) ? **Your answer:** - ⦿ \(-20\) - ⦿ \(-5\) - ⦿ The series diverges - ⦿ \(4\) Explanation: - The given expression is an infinite geometric series where the first term \(a = 4\) and the common ratio \(r = \frac{7}{6}\). - To determine whether the series converges or diverges, we need to examine the common ratio \(r\). For a geometric series to converge, the absolute value of the common ratio \(|r|\) must be less than 1. - In this case, \(\left|\frac{7}{6}\right| = \frac{7}{6} > 1\), which means the series does not converge. Instead, it **diverges**. Feel free to select your answer based on the provided options.
Transcribed Image Text:### Infinite Series Summation Problem **Question:** What is the value of \(\sum_{n=1}^{\infty} 4 \left(\frac{7}{6}\right)^{n-1}\) ? **Your answer:** - ⦿ \(-20\) - ⦿ \(-5\) - ⦿ The series diverges - ⦿ \(4\) Explanation: - The given expression is an infinite geometric series where the first term \(a = 4\) and the common ratio \(r = \frac{7}{6}\). - To determine whether the series converges or diverges, we need to examine the common ratio \(r\). For a geometric series to converge, the absolute value of the common ratio \(|r|\) must be less than 1. - In this case, \(\left|\frac{7}{6}\right| = \frac{7}{6} > 1\), which means the series does not converge. Instead, it **diverges**. Feel free to select your answer based on the provided options.
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