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?

Which rational numbers cannot be written in the form x + 1/(y +
1/z) where x, y and z are integers?

Golden Fractions

Age 16 to 18 Challenge Level

The hints are written into the question. If you can do a little
simple algebra, solve quadratic equations and argue through a proof
by induction, then you can sail through this question.