Do you know the future

Here, $f(x)=\frac{a^x}{a^x+\sqrt{a}}$

and, $f(1-x)=\frac{a^{1-x}}{a^{1-x}+\sqrt{a}}$

Note, that $f(x)+f(1-x)=1$

2[ $f(\frac{1}{2017})+f(\frac{2}{2017})+.............+f(\frac{2016}{2017})]$

$=2[f(\frac{1}{2017})+f(\frac{2016}{2017})+f(\frac{2}{2017})+f(\frac{2015}{2017})+......+f(\frac{1008}{2017})+f(\frac{1009}{2017})]$

$=2[f(\frac{1}{2017})+f(1-\frac{1}{2017})+f(\frac{2}{2017})+f(1-\frac{2}{2017})+......+f(\frac{1008}{2017})+f(1-\frac{1008}{2017})]$

$=2[1+1+1........\frac{2016}{2} times]$

$\boxed{2016}$