### 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?

### Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

### Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

# Reciprocal Values

##### Stage: 3 and 4 Short Challenge Level:
As $\frac{1}{x} = 3.5 = \frac{7}{2}$, so $x = \frac{2}{7}$.
Then $x+2 = \frac{16}{7}$.
Hence $\frac{1}{x+2} = \frac{7}{16}$.

This problem is taken from the UKMT Mathematical Challenges.
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