What is the value of E 4 7in-1 ? n- 1 Your answer:
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bfa811e-5464-4643-8887-727be93de7c9%2F2014edfb-3ea3-4faf-a0e6-3599651c1b52%2F9a0oc5c_processed.png&w=3840&q=75)
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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