Use the power series g(x)= = ∞ 1 1 + x to find a power series for the function, centered at 0. 1 x + 1 g(x) n = 0 ∞ = = • (-1)^x^, |x| < 1 n = 0 Determine the interval of convergence. (Enter your answer using interval notation.) (-1,1)
Use the power series g(x)= = ∞ 1 1 + x to find a power series for the function, centered at 0. 1 x + 1 g(x) n = 0 ∞ = = • (-1)^x^, |x| < 1 n = 0 Determine the interval of convergence. (Enter your answer using interval notation.) (-1,1)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 25RE
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Question
![Use the power series
g(x) =
1
1 + x
∞
Σ
n = 0
to find a power series for the function, centered at 0.
1
x + 1
=
g(x)
Σ+-15x",
Σ(-1)^x^, |x|<1
n = 0
Determine the interval of convergence. (Enter your answer using interval notation.)
(-1,1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb898cad9-5347-4e0a-a74d-32f84bfad0f6%2F126bcdb4-18af-4e7f-a0f9-2f28f7d15a31%2Fced28i_processed.png&w=3840&q=75)
Transcribed Image Text:Use the power series
g(x) =
1
1 + x
∞
Σ
n = 0
to find a power series for the function, centered at 0.
1
x + 1
=
g(x)
Σ+-15x",
Σ(-1)^x^, |x|<1
n = 0
Determine the interval of convergence. (Enter your answer using interval notation.)
(-1,1)
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