And So on - and on -and On

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
Let $$ f_{0}(x)= \frac{1}{1-x}$$ and $$f_{n}(x)=f_{0}(f_{n-1}(x))$$ where $n = 1,2, 3, 4, ...$

Evaluate $f_{2000}(2000)$

Published November 2004,December 2004.