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Algebra Level 4

$\large f(x) = \dfrac{(\sqrt{x} + 1)(x^{2} - \sqrt{x})}{x \sqrt{x} + x + \sqrt{x}}$

Define $f(x)$ as above and further define $g(x) = f(f(x))$ .

Find the value of $\large\displaystyle [\sum_{i=2}^{1000} g(i)] - 1$ .