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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![**Instruction:**
Find at least ten partial sums of the series. (Round your answers to five decimal places.)
\[
\sum_{n=1}^{\infty} \cos(6n)
\]
| \( n \) | \( s_n \) |
|---------|-----------|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 | |
**Explanation:**
- The series to be evaluated is an infinite series that involves the cosine function, where each term is \(\cos(6n)\), and \( n \) starts from 1.
- You are required to find the partial sums of this series for the first 10 terms.
- The notation \( s_n \) represents the \( n \)-th partial sum, which is the sum of the first \( n \) terms of the series. Calculate each \( s_n \) and round the result to five decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c92bfa8-de7b-4872-bcff-5b3a3db686c0%2F5c1f6561-efe5-4c7a-aec7-8a1095af49cb%2Ffup6j7_processed.png&w=3840&q=75)
Transcribed Image Text:**Instruction:**
Find at least ten partial sums of the series. (Round your answers to five decimal places.)
\[
\sum_{n=1}^{\infty} \cos(6n)
\]
| \( n \) | \( s_n \) |
|---------|-----------|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 | |
**Explanation:**
- The series to be evaluated is an infinite series that involves the cosine function, where each term is \(\cos(6n)\), and \( n \) starts from 1.
- You are required to find the partial sums of this series for the first 10 terms.
- The notation \( s_n \) represents the \( n \)-th partial sum, which is the sum of the first \( n \) terms of the series. Calculate each \( s_n \) and round the result to five decimal places.
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