Quiz 9
Name____________
Section___________
TA______________
Determine the radius of convergence as well as the precise interval of convergence for the power
series
2
0
(1
)
3
n
n
n
x
n
∞
=
+
∑
.
In other words, you should check the endpoints of the interval as well.
Please show all work.
2
2
12
21
2
1
1
)
3
1
2
(2
)
3
3
2
3
1
1
1
lim
2
33
1
nn
n
xx
xn
n
n
nx
n
n
n
n
ρ
+
+
→∞
⎛⎞
+
⎜⎟
++
==
⎝⎠
+
+
+
3
x
<⇒
absolutely convergent
3
x
>⇒
divergent
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This note was uploaded on 05/12/2008 for the course MATH 133 taught by Professor Wei during the Spring '07 term at Michigan State University.
 Spring '07
 Wei
 Calculus

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