已知函数f(x)=x^2/1+x^2求f(1)+f(2)+f(3)+f(4)+f(1/2)+f(1/3)+f(1/4)的值

f(1/x)=(1/x^2)/[1+(1/x^2)] 上下乘x^2 =1/(1+x^2) 所以f(x)+f(1/x) =x^2/(1+x^2)+1/(1+x^2) =(1+x^2)/(1+x^2) =1 所以f(1)+f(2)+f(3)+f(4)+f(1/2)+f(1/3)+f(1/4) =f(1)+1+1+1 =1/2+3 =7/2