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Math 1B Quiz 6 Solutions
Section 107
October 13, 2009
1. (4 points) Test the series for convergence or divergence:
∞
X
n
=1
tan

1
(1
/n
)
√
n
Use the Limit Comparison Test with the convergent pseries
1
n
3
/
2
. Calculate:
lim
n
→∞
tan

1
(1
/n
)
√
n
1
n
√
n
= lim
x
→∞
tan

1
(1
/x
)
1
x
= lim
x
→∞
(

1
/x
2
)
1
(1
/x
)
2
+1
(

1
/x
2
)
= 1
.
Since the limit is strictly between 0 and
∞
(0
<
1
<
∞
), the LCT applies. Therefore,
since
∑
1
n
3
/
2
converges,
∑
tan

1
(1
/n
)
√
n
converges.
2. (4 points) Test the series to determine whether it diverges, converges conditionally, or
converges absolutely.
∞
X
n
=1
(

1)
n
(3
1
/n
2

1)
n
Use the root test. Calculate:
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 Fall '08
 Reshetiken
 Math

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