Approximate the value of the series to within an error of at most 10-3. (-1)"+1 (n + 3)(n + 4) According to Equation (2): |SN - S| < aN+1 what is the smallest value of N that approximates S to within an error of at most 10-32 N = 29 S- 0.03084
Approximate the value of the series to within an error of at most 10-3. (-1)"+1 (n + 3)(n + 4) According to Equation (2): |SN - S| < aN+1 what is the smallest value of N that approximates S to within an error of at most 10-32 N = 29 S- 0.03084
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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![### Approximation of Series Sum with Error Margin
#### Problem Statement
Approximate the value of the series to within an error of at most \(10^{-3}\):
\[
\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{(n+3)(n+4)}
\]
#### Methodology
According to Equation (2):
\[
|S_N - S| \leq a_{N+1}
\]
#### Solution
To estimate \( S \) with an error margin of \( 10^{-3} \):
- **Smallest Value of \( N \)**: \( N = 29 \)
- **Approximate Value of \( S \)**: \( S \approx 0.03084 \)
The calculations and values ensure that the series approximation is accurate within the specified error margin \( 10^{-3} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7b1f94a-aeb1-4e21-a353-b14674dcbf02%2F36af7c40-0ee9-44ee-96a3-4592eefb140d%2Ffztsdpq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Approximation of Series Sum with Error Margin
#### Problem Statement
Approximate the value of the series to within an error of at most \(10^{-3}\):
\[
\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{(n+3)(n+4)}
\]
#### Methodology
According to Equation (2):
\[
|S_N - S| \leq a_{N+1}
\]
#### Solution
To estimate \( S \) with an error margin of \( 10^{-3} \):
- **Smallest Value of \( N \)**: \( N = 29 \)
- **Approximate Value of \( S \)**: \( S \approx 0.03084 \)
The calculations and values ensure that the series approximation is accurate within the specified error margin \( 10^{-3} \).
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