MAT 272
Test 4
Review
1.
Does each of the following geometric series converge or diverge?
If any converges, state the sum.
a)
n
1
n
2
)
4
1
(
∑
∞
=
b)
6 + 2 +
+
+
9
2
3
2
. . .
c)
n
3
n
n
4
3
)
1
(

∑
∞
=
2.
Does each of the following pseries converge or diverge?
a)
∑
∞
=
1
n
3
n
1
b)
∑
∞
=
1
n
4
n
1
c)
∑
∞
=
1
n
n
n
4
5
3.
Determine if each series below converges or diverges. State the test used and its results.
a)
∑
∞
=
⋅
+
1
n
n
3
4
n
)!
1
n
(
b)
∑
∞
=
+
+
1
n
5
4
2
n
8
1
n
3
c).
)
1
n
ln(
5
)
1
(
3
n
1
n
+

∑
∞
=
+
4.
Graph the first 10 terms of the sequence of partial sums for the series
(
29
∑
∞
=

1
n
1
n
4
.
3
.
What can you
conclude as to whether this series converges or diverges?
5.
Find the radius of convergence and the interval of convergence of the following series:
a)
∑
∞
=
+


0
n
n
n
1
n
)
3
x
(
)
1
(
b)
∑
∞
=
+
0
n
1
n
2
!
n
x
6.
Given that the power series for ln(x) is
∑
∞
=
+


1
n
n
1
n
n
)
1
x
(
)
1
(
,
a)
Find the interval of convergence.
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 Spring '08
 Rhee
 Geometric Series

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