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...
Related questions
Question
please show written work
![**Use Theorem 9.11 to determine the convergence or divergence of the p-series.**
\[ 1 + \frac{1}{\sqrt[7]{2}} + \frac{1}{\sqrt[7]{3}} + \frac{1}{\sqrt[7]{4}} + \ldots \]
**Explanation:**
This expression represents an infinite series where the terms are of the form \(\frac{1}{n^{1/7}}\) starting from \(n=2\). The question is asking to use Theorem 9.11, likely related to the properties of p-series, to determine whether this series converges or diverges. A p-series of the form \(\sum \frac{1}{n^p}\) converges if \(p > 1\) and diverges if \(p \leq 1\). In this case, \(p = \frac{1}{7}\), which is less than 1, suggesting divergence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45235a53-69d6-46fa-83a8-de0bf8bf66d1%2Fd368e7ff-e9a2-4a9e-ab0e-4f716fee3aa7%2Fo4x4isb_processed.png&w=3840&q=75)
Transcribed Image Text:**Use Theorem 9.11 to determine the convergence or divergence of the p-series.**
\[ 1 + \frac{1}{\sqrt[7]{2}} + \frac{1}{\sqrt[7]{3}} + \frac{1}{\sqrt[7]{4}} + \ldots \]
**Explanation:**
This expression represents an infinite series where the terms are of the form \(\frac{1}{n^{1/7}}\) starting from \(n=2\). The question is asking to use Theorem 9.11, likely related to the properties of p-series, to determine whether this series converges or diverges. A p-series of the form \(\sum \frac{1}{n^p}\) converges if \(p > 1\) and diverges if \(p \leq 1\). In this case, \(p = \frac{1}{7}\), which is less than 1, suggesting divergence.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning