∵f(x)=2x/(x+1),∴f(1/x)=(2/x)/(1/x+1)=2/(x+1),
∴f(x)+f(1/x)=2x/(x+1)+2/(x+1)=2(x+1)/(x+1)=2.
于是:
f(1)+f(2)+f(3)+······+f(100)+f(1/2)+f(1/3)+······+f(1/100)
=f(1)+[f(2)+f(1/2)]+[f(3)+f(1/3)]+······+[f(100)+f(1/100)]
=2×1/(1+1)+2×99
=1+2×(100-1)
=1+200-2
=199.