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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?

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Not Continued Fractions

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

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Comparing Continued Fractions

Which of these continued fractions is bigger and why?

And So on - and on -and On


The solution needs you to be systematic.

Start with $ f_{0} $, then work out $ f_{1}$, then work out $ f_{2}$

\begin{eqnarray}f_{0}(2000)&=& \frac{1}{1-2000}\\ &=& \frac{1}{-1999}\end{eqnarray}