3. We discussed in class that En-o(-1)"x"=1-x+x²-x³+...; if |x| < 1 Use that result to find the power series representation of the following functions, and determine their radius of convergence a) f(x) = 1+4 1+x b) f(x)= 1-x 1+x =
3. We discussed in class that En-o(-1)"x"=1-x+x²-x³+...; if |x| < 1 Use that result to find the power series representation of the following functions, and determine their radius of convergence a) f(x) = 1+4 1+x b) f(x)= 1-x 1+x =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Power Series Representation and Radius of Convergence**
**3. We discussed in class that**
\[
\frac{1}{1+x} = \sum_{n=0}^{\infty} (-1)^n x^n = 1 - x + x^2 - x^3 + \ldots \quad ; \quad \text{if} \quad |x| < 1
\]
Use that result to find the power series representation of the following functions, and determine their radius of convergence.
a) \( f(x) = \frac{1}{1+4x} \)
b) \( f(x) = \frac{1+x}{1-x} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff675898d-3fe8-40cd-9afe-fa982eda0648%2F0e8a5593-80c9-48d3-9b0c-d946c503d92c%2Fzhftdyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Power Series Representation and Radius of Convergence**
**3. We discussed in class that**
\[
\frac{1}{1+x} = \sum_{n=0}^{\infty} (-1)^n x^n = 1 - x + x^2 - x^3 + \ldots \quad ; \quad \text{if} \quad |x| < 1
\]
Use that result to find the power series representation of the following functions, and determine their radius of convergence.
a) \( f(x) = \frac{1}{1+4x} \)
b) \( f(x) = \frac{1+x}{1-x} \)
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