Functionally Odd

Algebra Level 4

f(x)=1x2+2x+13+x213+x22x+13\large f(x)=\dfrac{1}{\sqrt[3]{x^2+2x+1}+\sqrt[3]{x^2-1}+\sqrt[3]{x^2-2x+1}}

Find the value of the expression below.

f(1)+f(3)++f(997)+f(999)f(1)+f(3)+\cdots+f(997)+f(999)

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