Q14. Consider the power series (a). (b) n=1 (x - 1)" 3n √n +1 ] What is the center of this power series? (No justification needed.) ] Show that the radius of convergence of this power series is R = 3. Justify your answer, and clearly state the name the test you are using. (c) ] Determine the interval of convergence of this power series. Justify your answer, and clearly state the names of the tests you are using to determine convergence at the endpoints.
Q14. Consider the power series (a). (b) n=1 (x - 1)" 3n √n +1 ] What is the center of this power series? (No justification needed.) ] Show that the radius of convergence of this power series is R = 3. Justify your answer, and clearly state the name the test you are using. (c) ] Determine the interval of convergence of this power series. Justify your answer, and clearly state the names of the tests you are using to determine convergence at the endpoints.
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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![Q14. Consider the power series
(a).
(b)
n=1
(x - 1)n
3n √√n +1
What is the center of this power series? (No justification needed.)
] Show that the radius of convergence of this power series is R = 3. Justify your
answer, and clearly state the name the test you are using.
(c)
] Determine the interval of convergence of this power series. Justify your answer, and
clearly state the names of the tests you are using to determine convergence at the endpoints.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F177ac370-489a-423d-9b94-e0a7a4e4b992%2Fde1b708e-64bf-4592-8a8a-f37d5ce1a95a%2Fc53zvyi_processed.png&w=3840&q=75)
Transcribed Image Text:Q14. Consider the power series
(a).
(b)
n=1
(x - 1)n
3n √√n +1
What is the center of this power series? (No justification needed.)
] Show that the radius of convergence of this power series is R = 3. Justify your
answer, and clearly state the name the test you are using.
(c)
] Determine the interval of convergence of this power series. Justify your answer, and
clearly state the names of the tests you are using to determine convergence at the endpoints.
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