Discrete Mathematical Structures by Pearson

6-2 Discrete Mathematical Structures

1. 1, 1, 0, 0, 1, 1 is a finite sequence.

2. 1, 3, 5, 7, 9, 10, 12, 14 is a finite sequence.

3. 1,

1

2

,

1

3

,

1

4

,… is an infinite sequence.

4. 1, 3, 5, 7,… is an infinite sequence.

5. The sequence

1

2

,

1

4

,

1

8

,… can also be written as a

n

= 2

-n

, n ≥ 1

6. The sequence 1, -1, 1, -1,… can be written as a

n

= (-1)

n+1

,

n ≥ 1

7. The sequence 1, -1, 1, -1,… can be written as b

n

= (-1)

n

, n = 0, 1, 2…

Note 6.1

1. In a sequence, the elements may all be different or some of them may be repeated.

2. Some authors write the sequence starting with n = 0 instead of n = 1.

6.2.1 Recurrence Relation

Consider the sequence ...