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The University of Sydney
MATH 1004
Second Semester
Discrete Mathematics
2011
Tutorial 12 Week 13
1.
(
i
)
Show that
x
n
= 6
·
2
n

4 is a solution to the recurrence relation
x
n
= 3
x
n

1

2
x
n

2
.
(
ii
)
Show that
x
n
= (3
n
+1

1)
/
2 is a solution to the recurrence relation
x
n
+1

x
n
= 3
n
+1
.
(
iii
) Show that
x
n
=
n
! is a solution to the recurrence relation
x
n

n
(
n

1)
x
n

2
= 0
.
2.
Solve the following recurrence relations:
(
i
)
x
n

5
x
n

1
+ 6
x
n

2
= 0
, n
≥
2
, x
0
= 3
, x
1
= 7
(
ii
)
x
n

8
x
n

1
+ 16
x
n

2
= 0
, n
≥
2
, x
0
= 3
, x
1
= 20
.
3.
Solve the following recurrence relations:
(
i
)
x
n
= 10
x
n

1

25
x
n

2
, for
n
≥
2, where
x
0
=

1 and
x
1
= 5.
(
ii
)
x
n
+3

6
x
n
+2
+ 11
x
n
+1

6
x
n
= 0, for
n
≥
0, where
x
0
= 1,
x
1
= 0 and
x
2
=

1.
4.
Solve the following recurrence relations:
(
i
)
x
n
= 4
x
n

1

3
x
n

2
, where
x
0
= 1 and
x
1
= 2.
(
ii
)
x
n
= 3
x
n

1

3
x
n

2
+
x
n

3
, where
x
0
= 0,
x
1
= 1 and
x
2
= 3.
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View Full Document The University of Sydney
MATH 1004
Second Semester
Discrete Mathematics
2011
Problem Set 12
1.
Solve the following recurrence relations:
(
i
)
x
n
+ 6
x
n

1

7
x
n

2
= 0 for all
n
≥
2, with
x
0
= 1 and
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This note was uploaded on 09/01/2011 for the course YEAR 1 taught by Professor Various during the Three '11 term at University of Sydney.
 Three '11
 various

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