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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Question
![**Problem Statement:**
Find the 5th partial sum, \( s_5 \), of the series
\[
\sum_{n=2}^{\infty} (-1)^n
\]
**Solution:**
\[ s_5 = \boxed{0} \]
**Feedback:**
The answer provided, \( s_5 = 0 \), is incorrect (indicated by a red cross).
To find the correct 5th partial sum of the series \(\sum_{n=2}^{n=6} (-1)^n\), sum the terms from \(n = 2\) to \(n = 6\):
1. \(n = 2 \Rightarrow (-1)^2 = 1\)
2. \(n = 3 \Rightarrow (-1)^3 = -1\)
3. \(n = 4 \Rightarrow (-1)^4 = 1\)
4. \(n = 5 \Rightarrow (-1)^5 = -1\)
5. \(n = 6 \Rightarrow (-1)^6 = 1\)
Adding these values gives:
\[ 1 + (-1) + 1 + (-1) + 1 = 1 \]
Therefore, the correct value for \( s_5 \) should be \( \boxed{1} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0cfd4d2-3b60-4b70-8ad1-e02fd206eb06%2Fd579bf9d-3c02-45e0-9586-f0ee46b121f5%2F3p7dbkd_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the 5th partial sum, \( s_5 \), of the series
\[
\sum_{n=2}^{\infty} (-1)^n
\]
**Solution:**
\[ s_5 = \boxed{0} \]
**Feedback:**
The answer provided, \( s_5 = 0 \), is incorrect (indicated by a red cross).
To find the correct 5th partial sum of the series \(\sum_{n=2}^{n=6} (-1)^n\), sum the terms from \(n = 2\) to \(n = 6\):
1. \(n = 2 \Rightarrow (-1)^2 = 1\)
2. \(n = 3 \Rightarrow (-1)^3 = -1\)
3. \(n = 4 \Rightarrow (-1)^4 = 1\)
4. \(n = 5 \Rightarrow (-1)^5 = -1\)
5. \(n = 6 \Rightarrow (-1)^6 = 1\)
Adding these values gives:
\[ 1 + (-1) + 1 + (-1) + 1 = 1 \]
Therefore, the correct value for \( s_5 \) should be \( \boxed{1} \).
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