Tutorial Exercise Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) W (4x) no (3m)! Step 1 Recall the Ratio Test, which states that if a, is a series with nonzero terms, and lim <1, then a converges absolutely. If lim > 1, or lim =o, then diverges For any fixed value of x such that x = 0, let a (4x)" (3n)1 and find lim 918 (4x)+1 lim (3(n + 1))! = lim (4x) (an) lim (4x)+1 518 (3(n-1))! (3n)! 88,0 4x × (-00,00) X Step 2 By the Ratio Test, the series converges if lim -21. Therefore, the series converges for x such that lim an Submit Skip (you cannot come back)
Tutorial Exercise Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) W (4x) no (3m)! Step 1 Recall the Ratio Test, which states that if a, is a series with nonzero terms, and lim <1, then a converges absolutely. If lim > 1, or lim =o, then diverges For any fixed value of x such that x = 0, let a (4x)" (3n)1 and find lim 918 (4x)+1 lim (3(n + 1))! = lim (4x) (an) lim (4x)+1 518 (3(n-1))! (3n)! 88,0 4x × (-00,00) X Step 2 By the Ratio Test, the series converges if lim -21. Therefore, the series converges for x such that lim an Submit Skip (you cannot come back)
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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Transcribed Image Text:Tutorial Exercise
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
W
(4x)
no (3m)!
Step 1
Recall the Ratio Test, which states that if a, is a series with nonzero terms, and lim
<1, then a converges absolutely. If lim
> 1, or lim
=o, then diverges
For any fixed value of x such that x = 0, let a
(4x)"
(3n)1
and find lim
918
(4x)+1
lim
(3(n + 1))!
=
lim
(4x)
(an)
lim
(4x)+1
518 (3(n-1))!
(3n)!
88,0
4x
×
(-00,00)
X
Step 2
By the Ratio Test, the series converges if lim
-21. Therefore, the series converges for x such that lim
an
Submit Skip (you cannot come back)
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