Challenge Level

Given that $x$ is positive and less than $1$, list the following five 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.

You can find more short problems, arranged by curriculum topic, in our short problems collection.