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Algebra Level 4

f(x)=4x+4x212x+1+2x1\large f(x) = \dfrac {4x+\sqrt{4x^2-1}}{\sqrt{2x+1}+\sqrt{2x-1}}

Find the value of f(1)+f(2)++f(40)f(1) + f(2 ) + \cdots + f(40) .

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