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There's a Limit
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?
Not Continued Fractions
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
Age 16 to 18 Challenge Level:
When, if ever, is $${a\over b} + {c\over d} = {a+c\over b+d}$$ where $a$ and $b$ have no factors in common and $c$ and $d$ have no factors in common?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.