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?
Which of these continued fractions is bigger and why?
A well presented solution from Richard
of The Royal Hospital School reflected those of a number of other
solvers including Kevin of Langley Grammar, Jeff from New Zealand
and Andrei of Tudor Vianu School. Well done to all of