Question 9 Consider the series E(-1)"x": 1. |r| <1 or the series Ea" 1. I피 <1. 1+x n=0 n=0 (9.1) Use completion of the square and any of the above series to find a power series representation The series must be given in the form n(x – a)m+d. Also give the 1 bn+ for f(x) = 1² + 4x + 7) radius of convergence of this power series. (9.2) Every convergent power series is a Taylor series. Use only this fact and your answer in (9.1) to calculate f((-2).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question 9
Consider the series E(-1)"x":
1.
|r| <1 or the series Ea"
1.
I피 <1.
1+x
n=0
n=0
(9.1) Use completion of the square and any of the above series to find a power series representation
The series must be given in the form n(x – a)m+d. Also give the
1
bn+
for f(x) =
1² + 4x + 7)
radius of convergence of this power series.
(9.2) Every convergent power series is a Taylor series. Use only this fact and your answer in (9.1)
to calculate f((-2).
Transcribed Image Text:Question 9 Consider the series E(-1)"x": 1. |r| <1 or the series Ea" 1. I피 <1. 1+x n=0 n=0 (9.1) Use completion of the square and any of the above series to find a power series representation The series must be given in the form n(x – a)m+d. Also give the 1 bn+ for f(x) = 1² + 4x + 7) radius of convergence of this power series. (9.2) Every convergent power series is a Taylor series. Use only this fact and your answer in (9.1) to calculate f((-2).
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