Thread: Monotone sequence - how can this be a monotone sequence if it bounces between numbers

My understanding of showing a sequence is monotone is to show that it either increases or decreases by working out




and if it's > 0 its increasing, if less than, decreasing, right?

But now i have this problem that I must say if the sequence is monotone:




which to me works out that it is bounded by 0 and 4, ie that it bounces between 0 and 4 ( if n is odd then the value is 0 if even then its 4)

Surely this goes against monotone sequence??? But my answer says that it IS monotone. How can it be monotone when it is neither increasing nor decreasing??

A monotonically increasing sequence is one for which each term is greater than or equal to the term before it; if each term is strictly greater than the one preceding it, the sequence is called strictly monotonically increasing.

You have a monotonically increasing sequence since , but it's not strictly monitonically increasing.

Thanks, I was just replying as I picked up my error (I was confusing the with the original sequence. Ok I see it is increasing.

But what do you mean by "it is not strictly monotonically increasing?"

Thank you

In order for it to be strictly monitonically increasing, you need