(discrete math)
see the picture in the attachment.
how do i get started with this problem?

Recall the definition of the floor function: if is an integer and , then . So iff .

So let's consider four case.

First, suppose where . It follows that



because at most, we have



Meanwhile, , which follows immediately from



and so



Then for the second case, you can consider what happens when you have ; for the third, ; and for the fourth, .