Quick Review 9.5
1.
Converges, since it is of the form
E
‘
1
}
x
1
p
}
dx
with
p
.
1
2.
Diverges, limit comparison test with integral of
}
1
x
}
3.
Diverges, comparison test with integral of
}
1
x
}
4.
Converges, comparison test with integral of
}
x
2
2
}
5.
Diverges, limit comparison test with integral of
}
ˇ
1
x
w
}
6.
Yes, for
N
5
0
7.
Yes, for
N
5
2
ˇ
2
w
8.
No, neither positive nor decreasing for
x
.
ˇ
3
w
9.
No, oscillates
10.
No, not positive for
x
$
1
Section 9.5 Exercises
1.
Diverges by the Integral Test, since
E
‘
1
}
x
1
5
1
}
dx
diverges.
2.
Diverges because
∑
‘
n
5
1
}
ˇ
3
n
w
}
5
3
∑
‘
n
5
1
}
n
1
1/2
}
, which diverges by
the
p
series Test.
3.
Diverges by the Direct Comparison Test, since
}
ln
n
n
}
.
}
1
n
}
for
n
$
2 and
∑
‘
n
5
2
}
1
n
}
diverges.
4.
Diverges by the Integral Test, since
E
‘
1
}
2
x
1
2
1
}
dx
diverges.
5.
Diverges, since it is a geometric series with
r
5
}
ln
1
2
}
<
1.44.
6.
Converges, since it is a geometric series with
r
5
}
ln
1
3
}
<
0.91.
7.
Diverges by the
n
thTerm Test, since lim
n
→
‘
n
sin
}
1
n
}
5
1.
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 Spring '08
 GERMAN
 Mathematical Series, lim un, Diverges

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