(-4)2k+1 k3k-2 (* – 2)k. 5. Consider the power series k=1 (a) Find the radius and the interval of convergence of the series.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(-4)2k+1
k3k-2
5.
Consider the power series >,
-(x – 2)*.
k=1
(a)
Find the radius and the interval of convergence of the series.
(b)
Consider the function
f (x) =
(-4)2k+1
-(x – 2)*,
k3k-2
k=1
defined for all x in the interval of convergence. Find f(") (2) for all n > 0, and find a power series
representation for an antiderivative of f(x).
Transcribed Image Text:(-4)2k+1 k3k-2 5. Consider the power series >, -(x – 2)*. k=1 (a) Find the radius and the interval of convergence of the series. (b) Consider the function f (x) = (-4)2k+1 -(x – 2)*, k3k-2 k=1 defined for all x in the interval of convergence. Find f(") (2) for all n > 0, and find a power series representation for an antiderivative of f(x).
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