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Problem 2: Find a power series representation of f(x) = 2 centered at e= 0. What is the interval 4 + 7x of convergence for this power series? (Hint: convert the rational expression into the form , so that you can express it as a geometric series.)

Problem 2: Find a power series representation of f(x) = 2 centered at e= 0. What is the interval 4 + 7x of convergence for this power series? (Hint: convert the rational expression into the form , so that you can express it as a geometric series.)

Algebra & Trigonometry with Analytic Geometry
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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**Problem 2:** Find a power series representation of \( f(x) = \frac{2}{4 + 7x} \) centered at \( c = 0 \). What is the interval of convergence for this power series? (Hint: convert the rational expression into the form \( \frac{a}{1 - r} \) so that you can express it as a geometric series.)
Transcribed Image Text:**Problem 2:** Find a power series representation of \( f(x) = \frac{2}{4 + 7x} \) centered at \( c = 0 \). What is the interval of convergence for this power series? (Hint: convert the rational expression into the form \( \frac{a}{1 - r} \) so that you can express it as a geometric series.)
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