Radius of Convergence of a Power Series. (n!)x" Determine the radius of convergence for the series nn We begin by applying the Ratio Test to the series un, where un is the nth term of the power series in question and find that, Un+1 lim lim 11-700 Un 11-00 Note: type a simplified ratio in terms of x and n, then evaluate the limit above. Based on the results above, the radius of convergence of the power series is R
Radius of Convergence of a Power Series. (n!)x" Determine the radius of convergence for the series nn We begin by applying the Ratio Test to the series un, where un is the nth term of the power series in question and find that, Un+1 lim lim 11-700 Un 11-00 Note: type a simplified ratio in terms of x and n, then evaluate the limit above. Based on the results above, the radius of convergence of the power series is R
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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![Radius of Convergence of a Power Series.
Determine the radius of convergence for the series
(n!)x"
nn
We begin by applying the Ratio Test to the series Σun, where un is the nth term of the power series in
question and find that,
Un+1
P = lim
11-00 Un
nod
Note: type a simplified ratio in terms of x and n, then evaluate the limit above.
Based on the results above, the radius of convergence of the power series is R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd49a5070-9d99-4a2f-a144-be47e7ddead5%2F3dbc3675-abd7-4cf9-a98c-4e1a57be399c%2Fqhabrbb_processed.png&w=3840&q=75)
Transcribed Image Text:Radius of Convergence of a Power Series.
Determine the radius of convergence for the series
(n!)x"
nn
We begin by applying the Ratio Test to the series Σun, where un is the nth term of the power series in
question and find that,
Un+1
P = lim
11-00 Un
nod
Note: type a simplified ratio in terms of x and n, then evaluate the limit above.
Based on the results above, the radius of convergence of the power series is R
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