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f(x)=(x+1)(x2−x)xx+x+x\large f(x) = \dfrac{(\sqrt{x} + 1)(x^{2} - \sqrt{x})}{x \sqrt{x} + x + \sqrt{x}}f(x)=xx+x+x(x+1)(x2−x)
Define f(x)f(x) f(x) as above and further define g(x)=f(f(x))g(x) = f(f(x))g(x)=f(f(x)).
Find the value of [∑i=21000g(i)]−1\large\displaystyle [\sum_{i=2}^{1000} g(i)] - 1[i=2∑1000g(i)]−1.
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