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

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

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

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Example (4) Continue

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Example (6) Continue

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

Example (1)

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

Example (1)