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Use Theorem 9.11 to determine the convergence or divergence of the p-series 1 1 1 ਲੋਕ · + √3+√4 1 +7

Use Theorem 9.11 to determine the convergence or divergence of the p-series 1 1 1 ਲੋਕ · + √3+√4 1 +7

Calculus: Early Transcendentals
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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**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.
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.
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