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?
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?
This problem is taken from the UKMT Mathematical Challenges.View the archive of all weekly problems grouped by curriculum topic