2001 Problem!

Algebra Level 4

f(12001)+f(22001)+f(32001)++f(20002001)f \left( \frac 1{2001} \right) + f \left( \frac 2{2001} \right) + f \left( \frac 3{2001} \right) +\cdots + f \left( \frac {2000}{2001} \right)

Let f(x)=24x+2f(x) = \dfrac 2{4^x+2} for real numbers xx. Evaluate the expression above.

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