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.
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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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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