# Math Help - monotonic sequence

1. ## monotonic sequence

Hi,

A sequence { $a_n$} is called increasing if { $a_n$} < { $a_{n+1}$} for all $n \geq 1$. It is called decreasing if { $a_n$} > { $a_{n+1}$} for all $n \geq 1$. It is called monotonic if it is either increasing or decreasing.

Should that read "if it is *neither* increasing or decreasing." ?

It looks like a typo, but I'm not sure, so I thought I would ask for clarification. I tried some google searches but couldn't find a clear definition.

Thanks!

2. Nope that is correct.

3. A simple example of sequence that is 'neither increasing nor decreasing' is $a_{n}= (-1)^{n}\ \alpha^{n}$ , $\alpha > 0$...

Kind regards

$\chi$ $\sigma$

4. Originally Posted by centenial
Hi,

A sequence { $a_n$} is called increasing if { $a_n$} < { $a_{n+1}$} for all $n \geq 1$. It is called decreasing if { $a_n$} > { $a_{n+1}$} for all $n \geq 1$. It is called monotonic if it is either increasing or decreasing.