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11. The interval of convergence for the power series n=1 (a) 2 (x-1)". n-3n

11. The interval of convergence for the power series n=1 (a) 2 (x-1)". n-3n

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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**Question 11:** The interval of convergence for the power series \(\sum_{n=1}^{\infty} \frac{(x-1)^n}{n \cdot 3^n}\) is: (a) \(-2 < x < 4\) (b) \(-2 \leq x < 4\) (c) \(-2 < x \leq 4\) (d) \(-2 \leq x \leq 4\) (e) \(-2 < x < 4\) --- This question asks about determining the interval of convergence for the specified power series. The options provided give several possible intervals, using both strict inequalities ( < and > ) and inclusive inequalities ( \(\leq\) and \(\geq\) ). Careful examination and analysis of the power series are necessary to determine the accurate interval where the series converges.
Transcribed Image Text:**Question 11:** The interval of convergence for the power series \(\sum_{n=1}^{\infty} \frac{(x-1)^n}{n \cdot 3^n}\) is: (a) \(-2 < x < 4\) (b) \(-2 \leq x < 4\) (c) \(-2 < x \leq 4\) (d) \(-2 \leq x \leq 4\) (e) \(-2 < x < 4\) --- This question asks about determining the interval of convergence for the specified power series. The options provided give several possible intervals, using both strict inequalities ( < and > ) and inclusive inequalities ( \(\leq\) and \(\geq\) ). Careful examination and analysis of the power series are necessary to determine the accurate interval where the series converges.
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