Question

对于正数x,规定f(x)=x/(1+x),

Answer 1

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

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

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

所以

f(1/2009) + f(2009) = 1

f(1/2008) + f(2008) = 1

……

f(1/2) + f(2) = 1

f(1) + f(1) = 1

f(1/2009)+f(1/2008)+…+f(1/2)+f(1)+f(1)+f(2)+…+f(2008)+f(2009) = 2009