Unofficial
Math 31B Practice Final
by TA Ning Khamsemanan
Disclaimer:
this practice exam is my attempt to help you study for the
final. Things in here might not be in the real exam and vice versa. Don’t
use this as your main study. There might be some typos and/or mistakes.
1. Find the radius of convergence and Interval of convergence of the fol
lowing
(a)
∑
∞
n
=1
3
n
(
x

2)
n
(
n
+1)!
(b)
∑
∞
n
=1
(
x

1)
n
n
2
n
2. Find the power series representation of the following
(a) ln
1+
x
1

x
(b)
x
(1

2
x
)
2
3. Determine whether the following series if they are conditionally con
vergent, absolutely convergent or divergent.
(a)
∑
∞
n
=1
(

1)
n
(
n
+1)3
n
2
2
n
+1
(b)
∑
∞
n
=1
(

1)
n
+1
5
√
n
4. Test the series for convergence of divergence
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 Spring '09
 HOUDAYER
 Math, Power Series, Mathematical Series, TA, Ning Khamsemanan Disclaimer

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