You can justify your results using the Archimedean property
a) Prove that {n/1000} is an unbounded sequence. (I can tell obviously that it is unbounded because as n gets higher the whole sequence gets higher. But not sure how to formally prove this)
b) Is {n^2[[1000/n]]} an unbounded sequence? Explain.
(This is also unbounded right? Isnt this similar to the first one? If you distribute the n^2 in you get 1000n^2/n and then could just cancel an n from top and bottom and get 1000n as the sequence?)