f(m)+f(1/m)=m^2/(1+m^2)+(1/m^2)/(1+(1/m)^2)=m^2/(1+m^2)+1/(1+m^2)=1
f(1)+f2+f3+f4+f1/2+f1/3+f1/4=f1+f1+f2+f1/2+f3+f1/3+f4+f1/4=1+1+1+1=4