Use the power series Σ 1 1 + x 2(-1)^xn, \x| < 1 n = 0 to find a power series for the function, centered at 0. 1 f(x) = In(x + 1) =- x + 1 xp Σ f(x) n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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Use the power series
Σ
1
2(-1)^xn, Ix| < 1
n = 0
1 + x
to find a power series for the function, centered at 0.
1
f(x) = In(x + 1) = |-
x + 1
xp
Σ
f(x)
n = 0
Determine the interval of convergence. (Enter your answer using interval notation.)
Transcribed Image Text:Use the power series Σ 1 2(-1)^xn, Ix| < 1 n = 0 1 + x to find a power series for the function, centered at 0. 1 f(x) = In(x + 1) = |- x + 1 xp Σ f(x) n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)
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