Use the power series 1 1 + x Σ(-1)^xn, x < 1 n = 0 to find a power series for the function, centered at 0. f(x) = In(x + 1) f(x) = = 8 n = 0 8 = 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
Section: Chapter Questions
Problem 25RE
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Use the power series
∞
Σ (-1)^x^, |x| < 1
n = 0
to find a power series for the function, centered at 0.
f(x) = n(x + 1)
£
n = 0
f(x)
=
1
1 + x
Determine the interval of convergence. (Enter your answer using interval notation.)
Transcribed Image Text:Use the power series ∞ Σ (-1)^x^, |x| < 1 n = 0 to find a power series for the function, centered at 0. f(x) = n(x + 1) £ n = 0 f(x) = 1 1 + x Determine the interval of convergence. (Enter your answer using interval notation.)
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