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
What is the radius of convergence for the following series. Use the ratio test
![The image displays a mathematical expression of an infinite series:
\[
\sum_{n=0}^{\infty} \frac{x^{n+1}}{n!}
\]
### Explanation:
- **Summation Symbol (\(\sum\))**: This indicates that you're summing a series of terms from \(n = 0\) to infinity (\(\infty\)).
- **Term of the Series (\(x^{n+1}/n!\))**:
- **\(x^{n+1}\)**: This is \(x\) raised to the power of \(n+1\).
- **\(n!\)**: This represents the factorial of \(n\), which is the product of all positive integers up to \(n\).
This series is a mathematical structure often used in calculus and analysis, particularly in the study of power series and Taylor series expansions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F456fc56d-6522-4d21-af4e-8101a918b824%2F3ebf6d94-8e23-4895-9be0-ef915196fc13%2Fd5fw0vs_processed.png&w=3840&q=75)
Transcribed Image Text:The image displays a mathematical expression of an infinite series:
\[
\sum_{n=0}^{\infty} \frac{x^{n+1}}{n!}
\]
### Explanation:
- **Summation Symbol (\(\sum\))**: This indicates that you're summing a series of terms from \(n = 0\) to infinity (\(\infty\)).
- **Term of the Series (\(x^{n+1}/n!\))**:
- **\(x^{n+1}\)**: This is \(x\) raised to the power of \(n+1\).
- **\(n!\)**: This represents the factorial of \(n\), which is the product of all positive integers up to \(n\).
This series is a mathematical structure often used in calculus and analysis, particularly in the study of power series and Taylor series expansions.
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