sequences relating to cauchy and monotone.

Question

trying to come up with different examples on different situations I mean for example:

1. monotone sequence that is not convergent.
2. a convergent sequence that is not monotone.
3. a set that has no cluster points. (can I say Z?)
4. a bounded sequence that is not convergent. (can I say $(-1)^n$?)
5. a monotone sequence that is not cauchy.

help please!

Answer 1

1. Take the sequence $1,2,3,\ldots$
2. Take $\dfrac{(-1)^n}n$
3. You are right here.
4. Again, you are right here.
5. Again, take the sequence $1,2,3,\ldots$