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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 14 to 16
Challenge Level
Find the maximum of
$${1\over p} + {1\over q} + {1\over r}$$
where $p$, $q$ and $r$ are positive integers and
$${1\over p} + {1\over q} + {1\over r} < 1.$$
Prove that it is indeed a maximum.
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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.