f(x)+f(1/x)
=2x/(x+1)+2(1/x)/(1+1/x)
后面上下乘x
=2x/(x+1)+2/(x+1)
=2(x+1)/(x+1)
=2
所以f(1/2008)+f(2008)=2
f(1/2007)+f(2007)=2
……
f(1/2)+f(2)=2
f(1)=2/2=1
所以原式=2×2007+1=4015