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The series is absolutely convergent on the following interval. x-5 <1 |x - 5] < 10 x € (-5, 15) An alternating series is the series with the terms, in which the absolute value of all the terms decreases, is always a convergent series. An infinite series which is always divergent is called the harmonic series.

The series is absolutely convergent on the following interval. x-5 <1 |x - 5] < 10 x € (-5, 15) An alternating series is the series with the terms, in which the absolute value of all the terms decreases, is always a convergent series. An infinite series which is always divergent is called the harmonic series.

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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The center of the interval is a which equals 5 in this problem. Why would the radius of convergence be 15? for that to be true wouldn't the interval of convergence be (-10, 20) instead? I thought that R would equal 10.

The series is absolutely convergent on the following interval. x-5|<1 |x5| < 10 x € (-5, 15) An alternating series is the series with the terms, in which the absolute value of all the terms decreases, is always a convergent series. An infinite series which is always divergent is called the harmonic series. Atx = -5, the series becomes Σ (-1) (-10) = 1 which is divergent by nth term test. k=1 10k k=1 10k 10k At x = 15, the series becomes Σ(-1)*. n=1 = 00 k=1 (-1)* which is divergent by nth term test. 00 (-1)k Hence, the series > -(x - 5) converges on (-5, 15) and the radius of convergence is 15. 10k whyp
Transcribed Image Text:The series is absolutely convergent on the following interval. x-5|<1 |x5| < 10 x € (-5, 15) An alternating series is the series with the terms, in which the absolute value of all the terms decreases, is always a convergent series. An infinite series which is always divergent is called the harmonic series. Atx = -5, the series becomes Σ (-1) (-10) = 1 which is divergent by nth term test. k=1 10k k=1 10k 10k At x = 15, the series becomes Σ(-1)*. n=1 = 00 k=1 (-1)* which is divergent by nth term test. 00 (-1)k Hence, the series > -(x - 5) converges on (-5, 15) and the radius of convergence is 15. 10k whyp
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Given series ∑k=1∞(-1)k10k(x-5)k

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