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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
It is worth spending some time discussing the strategies pupils have adopted.
Another question might be:
What is the ratio of the speeds of the two runners if they are to meet at the start after $1$ lap, $2$ laps, $3$ laps... $n$ laps?.
What is the relationship betweent he ratio of the speeds of the runners and where they meet?
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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.