Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you
notice when successive terms are taken? What happens to the terms
if the fraction goes on indefinitely?

A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?

Largest Expression

Stage: 4 Short Challenge Level:

Given that $x$ is positive and less than $1$, we may deduce that
$$x^2+x > x^2+x^3 > x^2 > x^3 > x^4$$