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1. Determine whether the series is convergent or divergent. You may use
any of the tests we covered.
(a) (10 points)
Σ
n
=
∞
n
=1
n
2
n
(1 + 2
n
2
)
n
(b) (10 points)
Σ
n
=
∞
n
=1
3
n

1
2
n
+ 1
(c) (10 points)
Σ
n
=
∞
n
=1
n
2
+ 1
n
3
+ 1
(d) (10 points)
Σ
n
=
∞
n
=1
(

5)
2
n
n
2
9
n
2. (20 points) Determine whether the series is absolutely convergent, con
ditionally convergent, or divergent. You may use any of the tests we
covered.
Σ
n
=
∞
n
=2
(

1)
n
√
n
ln
(
n
)
3. (10 points) Suppose
f
(
x
) is a positive decreasing function and let
a
n
=
f
(
n
),
n
≥
1. Draw a picture which explains how to rank the following
three quantities in increasing order
i
4
1
f
(
x
)
dx,
Σ
i
=3
i
=1
a
i
,
Σ
i
=4
i
=2
a
i
4. (20 points) Find the radius of convergence and the interval of conver
gence.
Σ
n
=
∞
n
=1
2
n
(
x

2)
n
(
n
+ 2)!
1
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View Full Document 5. Suppose Σ
n
=
∞
n
=0
c
n
x
n
converges for
x
=

3 and diverges for
x
= 5. What
can be said about the convergence/divergence of the following series?
Why?
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This test prep was uploaded on 04/07/2008 for the course MATH 1 taught by Professor Johns during the Spring '08 term at NYU.
 Spring '08
 Johns
 Calculus

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