Use the power series E(-19^x", \xl < 1 n-0 to find a power series for the function, centered at 0. (x) = In(x® + 1) (x) = (-1)" „Sn+8 n+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 22RE
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Use the power series
1
1 + X
x = 2 (-1)^xn, \x| < 1
n = 0
to find a power series for the function, centered at 0.
f(x) = In(x8 + 1)
F(x) =
Σ
(-1)" 8n+8
n + 1
n = 0
Determine the interval of convergence. (Enter your answer using interval notation.)
(-1,1)|
Transcribed Image Text:Use the power series 1 1 + X x = 2 (-1)^xn, \x| < 1 n = 0 to find a power series for the function, centered at 0. f(x) = In(x8 + 1) F(x) = Σ (-1)" 8n+8 n + 1 n = 0 Determine the interval of convergence. (Enter your answer using interval notation.) (-1,1)|
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