•
I
•
I
•
I
•
C
•
C
•
I
3.
(1 pt)
Consider the series
∞
∑
n
=
1
1
n
(
n
+
3
)
Determine whether the series converges, and if it converges,
determine its value.
Converges (y/n):
Value if convergent (blank otherwise):
Correct Answers:
•
Y
•
0.611111111111111
4.
(1 pt) Match each of the following with the correct state
ment.
C stands for Convergent, D stands for Divergent.
1.
8
n
2.
∞
∑
n
=
1
1
2
+
4
√
n
6
3.
∞
∑
n
=
2
2
n
8

9
4.
∞
∑
n
=
1
2
n
(
n
+
3
)
5.
∞
∑
n
=
1
8
+
7
n
8
+
2
n
∞
∑
n
=
1
ln
(
n
)
1
1
n
diverges, so
by the Comparison Test, the series
∑
ln
(
n
)
n
diverges.
6. For all
n
>
2,
ln
(
n
)
n
2
>
1
n
2
, and the series
∑
1
n
2
converges,
so by the Comparison Test, the series
∑
ln
(
n
)
n
2
converges.
5.
(1 pt) Use the ratio test to determine whether
∞
∑
n
=
14
n
+
9
n
!
converges or diverges.
(a) Find the ratio of successive terms.
Write your answer as
a fully simplified fraction. For
n
≥
14,
lim
n
→
∞
a
n
+
1
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(b) Evaluate the limit in the previous part. Enter
∞
as
infinity
and

∞
as
infinity.
If the limit does not exist, enter
DNE.
(c) By the ratio test, does the series converge, diverge, or is
the test inconclusive?
?
6.
(1 pt) Use the ratio test to determine whether
2
n
converges or diverges.
(a) Find the ratio of successive terms.
Write your answer as
a fully simplified fraction. For
n
≥
26,
lim
n
(b) Evaluate the limit in the previous part. Enter
∞
as
infinity
and

∞
as
infinity.
If the limit does not exist, enter
DNE.
(c) By the ratio test, does the series converge, diverge, or is
the test inconclusive?
?