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Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition or description with a graph or an algebraic example.

A bounded sequence

Short Answer

Expert verified

A sequence anis a bounded sequence if it is bounded above and bounded below. If a sequence is not bounded, it is an unbounded sequence.

For example, the sequence -1nis bounded.

Step by step solution

01

Step 1. Given Information  

The given statement is a bounded sequence.

02

Step 2. Explanation 

A sequence anis bounded aboveif there exists a real number M such that anMfor all positive integers n.

A sequence an is bounded below if there exists a real number M such that

Manfor all positive integers n.

A sequence anis a bounded sequence if it is bounded above and bounded below. If a sequence is not bounded, it is an unbounded sequence.

For example, the sequence-1nis bounded.

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