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Logarithmic p-series a. Show that the improper integral dx (p a positive constant) x (In x)" converges if and only if p > 1. b. What implications does the fact in part (a) have for the con- vergence of the series n (In n)P n= Give reasons for your answer.

Logarithmic p-series a. Show that the improper integral dx (p a positive constant) x (In x)" converges if and only if p > 1. b. What implications does the fact in part (a) have for the con- vergence of the series n (In n)P n= Give reasons for your answer.

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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Logarithmic p-series a. Show that the improper integral dx (p a positive constant) x (In x)" converges if and only if p > 1. b. What implications does the fact in part (a) have for the con- vergence of the series n (In n)P n= Give reasons for your answer.
Transcribed Image Text:Logarithmic p-series a. Show that the improper integral dx (p a positive constant) x (In x)" converges if and only if p > 1. b. What implications does the fact in part (a) have for the con- vergence of the series n (In n)P n= Give reasons for your answer.
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