What is a Monotonic Sequence?
In some sequence theory, they define a monotonic sequence to be the sequence of numbers where the term is bigger or equal to the previous term or is lesser or equal to the previous term. Therefore if one aims at identifying if a sequence is monotonic what it means is whether the sequence is strictly increasing or decreasing. Formally, a sequence {an} is monotonic if either a{n+1} ≥ an for all n ≥ 1 (increasing) or a{n+1} ≤ an for all n ≥ 1 (decreasing). Specifically, monotonic sequences have the characteristic that the direction of their changes at any point is positively oriented, which implies that sequences of this type are either constantly on the rise or are progressively declining.
Monotonic Sequence
Monotonic sequence is one of the simplest terms used in mathematics to refer to a number sequence that moves from a smaller value to a bigger value or vice versa; that is, it only increases or decreases. Different fields of study where this type of sequence is important include calculus, probability and computer science. Mastering monotonically increasing and decreasing sequences is particularly important for studying the convergence and behavior of mathematical functions and series.
In this article, we will learn in detail about monotonic sequence, theorem, types and examples.
Table of Content
- What is a Monotonic Sequence?
- Types of Monotonic Sequence
- Monotonic Sequence Example and Graph
- Monotonic Sequence Theorem
- Bounded and Monotonic sequence
- Comparing Monotonic Sequences