saliyev (is4663) – Quest Assignment 6 – rodin – (54520)
1
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001
10.0 points
If
a
n
, b
n
,
and
c
n
satisfy the inequalities
0
< a
n
≤
c
n
≤
b
n
,
for all
n
, what can we say about the series
(
A
) :
∞
n
= 1
a
n
,
(
B
) :
∞
n
= 1
b
n
if we know that the series
(
C
) :
∞
n
= 1
c
n
is divergent but know nothing else about
a
n
and
b
n
?
1.
(
A
) diverges
,
(
B
) need not diverge
2.
(
A
) need not diverge
,
(
B
) diverges
3.
(
A
) converges
,
(
B
) diverges
4.
(
A
) converges
,
(
B
) need not converge
5.
(
A
) diverges
,
(
B
) converges
6.
(
A
) diverges
,
(
B
) diverges
002
10.0 points
Which of the following series
(
A
)
∞
n
= 1
3
5
n
log
n
+ 6
n
(
B
)
∞
n
= 1
6
n
n
(
n
+ 3)
n
(
C
)
∞
n
= 1
3
n
5
n
+ 3
n
diverge?
1.
C
only
2.
A
and
C
3.
all of them
4.
A
only
5.
A
and
B
003
10.0 points
Determine whether the series
∞
k
= 1
tan

1
k
6 +
k
3
converges or diverges.
1.
series is divergent
2.
series is convergent
004
10.0 points
Which of the following series
(
A
)
∞
n
= 1
(5 sin
n
)
2
2
n
2
+ 2
(
B
)
∞
n
= 1
5
n
8
n
2
ln
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 Fall '07
 Sadler
 Sequences And Series, Summation, n=1, Indian mathematics

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