help with liminf and limsup

PvtBillPilgrim3

This isn't a copy of my assignment, but I found the exact same question on the web:

http://www.math.auckland.ac.nz/~waldron/730/1.pdf

It's question 1 on the PDF. I've been trying all night to find inequalties that are strict like it asks for in that particular problem. I don't need help with proving the inequalities, just an example of two sequences (xn) and (yn) that satisfy them to make them strict simultaneously.

I would super appreciate any ideas on this.
I just need help where it says: Find sequences for which all of these inequalities are simultaneously strict. I can't find an example.

zhentil

Under what conditions does limsup = liminf?