Find a formula for the power series of ƒ(x) = 2 ln (1 + x), −1 < x < 1 in the form Σan. n=1 2 1 + x (Express numbers in exact form. Use symbolic notation and fractions where needed.) Hint: First, find the power series for g(x) = Then integrate.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
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Find a formula for the power series of f(x) = 2 ln (1 + x), −1 < x < 1 in the form
Hint: First, find the power series for g(x)
2
1 + x
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
an =
=
.
∞
Then integrate.
n=1
an.
Transcribed Image Text:Find a formula for the power series of f(x) = 2 ln (1 + x), −1 < x < 1 in the form Hint: First, find the power series for g(x) 2 1 + x (Express numbers in exact form. Use symbolic notation and fractions where needed.) an = = . ∞ Then integrate. n=1 an.
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