
The Remarkable Number 1/89 (2004) - archibaldJ
http://www2.math.ou.edu/~dmccullough/teaching/miscellanea/miner.html
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impendia
This works because of _generating functions_ : You can check that

1/(1 - x - x^2) = 1 + x + 2 _x^2 + 3_ x^3 + 5 _x^4 + 8_ x^5 + 13 _x^6 + 21_
x^7 + ...

To check this (not totally rigorously), multiply both sides by 1 - x - x^2 and
multiply everything out. On the right side the recurrence relation implies
that everything but the first term will cancel out.

So you can also get, for example,

1/9899 = 0.0001010203050813213455...

1/998999 = 0.000001002003005008013021034055089144233...

and so on.

