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DiscGQ02 – gilbert – (55035)
1
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001
10.0 points
Determine whether the series
1 + 3 + 9 + 27 + · · ·
is convergent or divergent, and if
convergent, find its sum.
1. convergent with sum
=
2
9
2. divergent correct
3. convergent with sum
=
2
4. convergent with sum
=
9
2
5. convergent with sum
=
1
2
Explanation:
The series
∞
1 + 3 + 9 + 27 + · · ·
=
A R
N
−1
N
=1
is an infinite geometric series in which A
= 1 and R = 3. But such a series is
A
(i) convergent with sum
1
−
R
when R < 1,
(ii) divergent when R ≥
1 . Thus the given series is
divergent
.
and the series
11
B
=
F (N) .
N
= 6
1. A
<
B
2. A
>
B correct
3. A
=
B
Explanation:
In the figure
A
6
A
7
A
8
A
9
. . .
5
6
7
8
9
the bold line is the graph of F on [5, ∞)
and
the
areas
of
the
rectangles
the
terms in the series
∞
A
N
,
A
N
= F (N) .
N
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 Spring '07
 Sadler

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