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136
Solutions to Exercises
(d) This is the sum of a geometric sequence with
a
=
1, r
=
!.
Solving
~
=
ar
n

1
,
we get
n
=
61, so the sum is
1(_!)61 _
~(
~)
1
(_!) 
3 1
+
261
.
(e) This is the sum of a geometric sequence with
a
=
2,
r
=
3. Noting that 354294
=
2(3
11
)
and
solving
ar
n

1
=
354294, we get
n
=
12. So the sum is
2(1 3
12
)
=
3
12
_1.
13
34. (a)
[BB]
This is the sum of an arithmetic sequence with
a
=
1004 and
d
=
3. With
an
= 397 =
a
+
(n
l)d,
we have 1004 
3(n
1)
= 397,
so
3(n
1)
=
1401,
n
1
=
467, so
n
=
468.
.
n
468
The sum
IS
S
=
"2[2a
+
(n
l)d]
=
2[2008
+
467( 3)]
=
234(607)
=
142038.
(b) This is the sum of a geometric sequence with
a
=
324 and r
=
~.
Solving
ar
n

1


131072
gives
(_~)nl

32768
so
n
 1
=
15
n
=
16

177147
3

14348907'
,.
The sum is
a(l rn)
324(1
(_~)16)
324(1
(~)16)
3(324)(1
(~)16)
34384948
=
2
=
5
=
=
1r
1('3) '3 5 177147
35.
[BB]
Suppose the arithmetic sequence
ao, ao
+
d, ao
+
2d, .
.. is also the geometric sequence
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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