f(1/n)=(1/n)^2/[1+(1/n)^2]=1/(1+n^2)
f(n)=n^2/(1+n^2)
f(1/n)+f(n)=1
f(1)=1/2
f(1)+f(2)+f(3)+...+f(n)+f(1/2)+f(1/3)+...+f(1/n)
=f(1)+f(2)+f(3)+...+f(n)+f(1/1)+f(1/2)+f(1/3)+...+f(1/n)-f(1/1)
=n-1/2
f(1/n)=(1/n)^2/[1+(1/n)^2]=1/(1+n^2)
f(n)=n^2/(1+n^2)
f(1/n)+f(n)=1
f(1)=1/2
f(1)+f(2)+f(3)+...+f(n)+f(1/2)+f(1/3)+...+f(1/n)
=f(1)+f(2)+f(3)+...+f(n)+f(1/1)+f(1/2)+f(1/3)+...+f(1/n)-f(1/1)
=n-1/2