Determine whether the series
∞
summationdisplay
n
=1
a
n
converges or diverges.
1.
converges
2.
diverges
3.
neither converges nor diverges
008
10.0points
Which one of the following properties does
the series
∞
summationdisplay
n
=3
(

1)
n
4
n
(ln
n
)
n
have?
1.
absolutely convergent
2.
conditionally convergent
3.
divergent
009
10.0points
Find all integers
m >
1 for which both of
the infinite series
∞
summationdisplay
n
=1
(

1)
mn
2
n
+ 6
,
∞
summationdisplay
n
=1
parenleftBig
m
11
parenrightBig
n
converge.
1.
m
= 3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
2.
m
= 2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
3.
m
= 3
,
5
,
7
,
9
4.
m
= 2
,
4
,
6
,
8
,
10
5.
m
= 3
,
5
,
7
,
9
,
11
fernando (rf9447) – HW03 – kalahurka – (55295)
3
010
10.0points
Decide whether the series
∞
summationdisplay
n
=1
11
n
parenleftBig
n

2
n
parenrightBig
n
2
converges or diverges.
1.
converges
2.
diverges
011
10.0points
Which one of the following properties does
the series
∞
summationdisplay
n
=1
parenleftbigg
4

3
n
2
4 + 5
n
2
parenrightbigg
n
have?
1.
divergent
2.
absolutely convergent
3.
conditionally convergent
012
10.0points
Determine whether the series
∞
summationdisplay
n
=0
(

8)
n
(2
n
)!
is absolutely convergent, conditionally con
vergent, or divergent.
1.
divergent
2.
absolutely convergent
3.
conditionally convergent
013
10.0points
To apply the ratio test to the infinite series
summationdisplay
n
a
n
, the value of
λ
=
lim
n
→ ∞
a
n
+1
a
n
has to be determined.
Compute
λ
for the series
∞
summationdisplay
n
=1
(
n
!)
2
(2
n
)!
parenleftbigg
2
3
parenrightbigg
n
.
1.
λ
=
2
3
2.
λ
=
1
3
3.
λ
=
4
3
4.
λ
=
2
9
5.
λ
=
1
6
014
10.0points
Which one of the following properties does
the series
1

1
·
3
3!
+
1
·
3
·
5
5!

1
·
3
·
5
·
7
7!
+
. . .
+ (

1)
n
1
·
3
· · · ·
(2
n

1)
(2
n

1)!
+
. . . .
have?
1.
absolutely convergent
2.
conditionally convergent
3.
divergent
015
10.0points
To apply the root test to an infinite series
summationdisplay
n
a
n
the value of
ρ
=
lim
n
→ ∞
(
a
n
)
1
/n
fernando (rf9447) – HW03 – kalahurka – (55295)
4
has to be determined.
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 Fall '07
 Fakhreddine/Lyon
 Mathematical Series, Radius of convergence