对于正数x,规定f(x)=x/(1+x),

来源：百度知道 编辑：UC知道 时间：2024/05/24 11:56:53
例如f(3)=3/(1+3)=3/4,f(1/3)=(1/3)/(1+1/3)=1/4.计算:f(1/2009)+f(1/2008)+…+f(1/2)+f(1)+f(1)+f(2)+…+f(2008)+f(2009)

计算:f(1/2009)+f(1/2008)+…+f(1/2)+f(1)+f(1)+f(2)+…+f(2008)+f(2009)

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

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

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

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)