Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Question
Question 4 please
Transcribed Image Text:8.2 EXERCISES
In Problems 1-6, determine the convergence set of the given
power series.
2™"
1. Σ -(x-1)"
n=on + 1
Q
to. Al
hood of xo to a function has to be the Taylor series of that function. For example, the expar
for arctan x given in (9) of Example 2 must be its Taylor expansion.
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With these facts in mind we are ready to turn to the study of the effectiveness of
series techniques for solving differential equations. In the next sections, you will find it hel
to keep in mind that if fand g are analytic at xo, then so are f+g, cf, fg, and f/g if g(x) =
These facts follow from the algebraic properties of power series discussed earlier.
12
3
2.
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n=on!"
4
R
21-22
X²
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5
T
6
When the expansion point xo is zero, the Taylor series is also known as the Maclaurin series.
X
&
7
00
3.
Σ(x+2)"
3
5. Σ'(x-2)"
n=1 n
n=0
8
1
(
9
I 4.
)
6.
00
4
Σ
n=1n² + 2n
(n+2)!
n!
$10
∞o
n=0
-(x-3)"
-(x + 2)"
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