1. Boundedness from Above A sequence is said to be bounded from above if there exists a real number, c such that : S n ≤ c, nεN

2. A sequence is said to be bounded from below if there exists a real number c such that : c ≤ S n ; nεN Boundedness from Below

3. A sequence is said to be bounded if it is bounded both from above and from below. That’s if there are real numbers c 1 a and c 2 such that: c 1 ≤ S n ≤ c 2 ; nεN This is equivalent to say that is bounded if there is a real number c such that: | S n | ≤ c ; nεN Boundedness

4. Example (1)

5. Example (2)

6. Example (3)

7. Example (4)

8. Example (4) Continue

9. Example (5)

10. Example (6)

11. Example (6) Continue

12. Unboundedness from Above A sequence is said to be unbounded from above if there f any positive number c, exists a term S N of the sequence such that : S N > c This equivalent to saying that for any natural number exists a term S N of the sequence such that : S N > n

13. Example (1)

14. Unboundedness from Below A sequence is said to be unbounded from below if there f any positive number c, exists a term S N of the sequence such that : S N < - c This equivalent to saying that for any natural number exists a term S N of the sequence such that : S N > n

15. Example (1)