# Thread: What Is A Monotonic Sequence?

1. ## What Is A Monotonic Sequence?

What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?

2. Originally Posted by fattydq
What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?
A sequence $\{a_n\}$ is monotonic if $a_{i + 1}\geq a_i$ or $a_{i + 1} \leq a_i$ for all $i \geq 1$.

3. Originally Posted by fattydq
What exactly is a Monotonic Sequence? Could someone give me an example of both a sequence that IS monotonic and one that ISN'T?
For example,

{1, 1, 1, 1, ...} is monotonic since $a_{i+1}=a_i$

{1 , 2, 3, 4, ...} is monotonic since $a_{i+1}>a_i$

{1, -1, 1, -1,...} is not monotonic since that does not satisfy the definition.
By the way, some texts use the term "strictly monotone" to distinguish the case " $a_{n+1}> a_n$" or " $a_{n+1}< a_n$" from " $a_{n+1}\ge a_n$" or " $a_{n+1}\le a_n$".
Other texts use "monotone" only for " $a_{n+1}> a_n$" or " $a_{n+1}< a_n$" and use "non-decreasing" for " $a_{n+1}\ge a_n$" and "non-increasing" for " $a_{n+1}\le a_n$".