2016 problem!

Algebra Level 5

f(12016)+f(22016)+f(32016)++f(20162016)f \left( \frac 1{2016} \right) + f \left( \frac 2{2016} \right) + f \left( \frac 3{2016} \right) +\cdots + f \left( \frac {2016}{2016} \right)

Let f(x)=816x+4f(x) = \dfrac 8{16^x+4} for real numbers xx. Evaluate the expression above.

Submit your answer to three decimal places.

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