1 3. We have shown in class that f(x)=- Ex" for all values of x in (-1,1) . 1-x n=0 а) Determine a function that would be represented by the power series En(n-1)x"-². n=2 b) What is the radius of convergence of this power series? n-2 c) Use your knowledge from parts (a) and (b) to determine the sum of the series En(n-1)| ÷| n=2

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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3. We have shown in class that ƒ (x)=.
Ex" for all values of x in (-1,1).
1-x
n=0
a)
Determine a function that would be represented by the power series En(n-1)x"² .
n=2
b)
What is the radius of convergence of this power series?
n-2
Use your knowledge from parts (a) and (b) to determine the sum of the series n(n-1) -|
n=2
Transcribed Image Text:3. We have shown in class that ƒ (x)=. Ex" for all values of x in (-1,1). 1-x n=0 a) Determine a function that would be represented by the power series En(n-1)x"² . n=2 b) What is the radius of convergence of this power series? n-2 Use your knowledge from parts (a) and (b) to determine the sum of the series n(n-1) -| n=2
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