A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.

Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.

Challenge Level

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 $f_{2000}(2000)$

Evaluate $f_{2000}(2000)$

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