Recall that the radius of convergence R of a power series with coefficients a, is found by first computing an+1 L = lim an n+00 and then computing 1 R= L' subject to the convention that if L = 0, then R = o and if L = 0, then R = 0. Consider the two power series E(-1)" and (-1)^ (* – 2)". n=1 (1) Computo thO radius of nvorgonco of onch sorios
Recall that the radius of convergence R of a power series with coefficients a, is found by first computing an+1 L = lim an n+00 and then computing 1 R= L' subject to the convention that if L = 0, then R = o and if L = 0, then R = 0. Consider the two power series E(-1)" and (-1)^ (* – 2)". n=1 (1) Computo thO radius of nvorgonco of onch sorios
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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![Recall that the radius of convergence R of a power series
with coefficients a, is found by first computing
An+1
L = lim
an
and then computing
R
L'
subject to the convention that if L = 0, then R = x and if L = oo,
then R = 0. Consider the two power series
(-1)"
and (-1)- (- 2)"
n=1
(1) Compute the radius of convergence of each series.
(2) Does the first series converge when r = 1/2? Does the second
series converge with r 1/2? Provide a brief justification for
your answer based on the result of the previous item.
(3) Determine the interval of convergence of the first series.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80de8ac7-b2da-460a-8c7f-97c5e2e8478e%2Fdbe58d7f-6a7e-4eb1-866c-ad8f9f9f5368%2Ffqey23g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Recall that the radius of convergence R of a power series
with coefficients a, is found by first computing
An+1
L = lim
an
and then computing
R
L'
subject to the convention that if L = 0, then R = x and if L = oo,
then R = 0. Consider the two power series
(-1)"
and (-1)- (- 2)"
n=1
(1) Compute the radius of convergence of each series.
(2) Does the first series converge when r = 1/2? Does the second
series converge with r 1/2? Provide a brief justification for
your answer based on the result of the previous item.
(3) Determine the interval of convergence of the first series.
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