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
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
![The image features a mathematical expression representing an infinite series:
\[
\sum_{n=1}^{\infty} \frac{10^n}{(-9)^{n-1}}
\]
### Explanation:
- **Summation Symbol (\(\sum\))**: This indicates a series, with terms summed from \(n = 1\) to infinity (\(\infty\)).
- **Expression for Each Term**:
- The numerator is \(10^n\), which signifies \(10\) raised to the power of \(n\).
- The denominator is \((-9)^{n-1}\), meaning \(-9\) is raised to the power of \((n - 1)\).
This series is an example of a geometric series, and evaluating it involves determining if it is convergent or divergent based on its common ratio.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F400422d1-8758-4e07-b9a5-d2a083bc6c63%2Ffab3adbf-dcbd-4459-997d-4016042dfb57%2Fhqanex_processed.png&w=3840&q=75)
Transcribed Image Text:The image features a mathematical expression representing an infinite series:
\[
\sum_{n=1}^{\infty} \frac{10^n}{(-9)^{n-1}}
\]
### Explanation:
- **Summation Symbol (\(\sum\))**: This indicates a series, with terms summed from \(n = 1\) to infinity (\(\infty\)).
- **Expression for Each Term**:
- The numerator is \(10^n\), which signifies \(10\) raised to the power of \(n\).
- The denominator is \((-9)^{n-1}\), meaning \(-9\) is raised to the power of \((n - 1)\).
This series is an example of a geometric series, and evaluating it involves determining if it is convergent or divergent based on its common ratio.
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