What is important about monotonic and bounded sequences?

Alex Cervantes

Alex Cervantes

Answered question

2022-01-25

What is important about monotonic and bounded sequences?

Answer & Explanation

pripravyf

pripravyf

Beginner2022-01-26Added 12 answers

A sequence is said to be monotonic, if it is either monotonically increasing or decreasing.
A sequence, an is monotonic increasing if an+1annN.
A sequence, an is monotonic decreasing if an+1annN
A Sequence, an is bounded if there exist number M>0 such that, anMnN
By Monotone Convergence Theorem, a monotone sequence of real numbers is convergent if it is bounded. By using this, one can say that every monotone bounded sequence are convergent.

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