# Dirty Polynomial (200 followers problem)

Algebra Level 5

$$P(x)$$ is a polynomial of degree 200. It is known that $$P\left( x \right) =\frac { x-2 }{ { x }^{ 2 }+1 }$$ for all integers $$x$$ in the domain $$-20<x<20$$.

Find the sum of all coefficients of terms with even degree in the expansion of $$P(x)$$.

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