Given that $x$ is positive and less than $1$, list the following expressions from smallest to largest:
$x^2 + x$, $x^2$, $x^3$, $x^3 + x^2$, $x^4$.
If you liked this problem, here is an NRICH task
which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.