Summing a function

Algebra Level 3

Let

f(x)=24x+2f (x) = \frac {2}{4^x + 2}

for all real numbers xx. Evaluate

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

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