Question

如果记y=x/(x+1),并且f(√ 1)表示x=√ 1时y的值.即f(√ 1)=√ 1/(√ 1+1)=1/2；f（√

Answer 1

f(x)=x/(x+1)

f(1/x)=(1/x)/(1/x+1)=1/(x+1)

∴f(x)+f(1/x)=1

f（√1）+f（√2)+f(√3)+...+f(√2012)+f(√1/√2)+f(√1/√3)+...+f(√1/√2012)

=f(√1)+ [(f(√2)+f(1/√2)]+ [(f(√3)+f(1/√3)]+……+ [(f(√2012)+f(1/√2012)]

=1/2+1+1+……+1

=2011+1/2

=2011又1/2