f(1/2)-f(1/2)=f((1/2-1/2)/(1-1/4))=f(0)=0
-f(x)=f(0)-f(x)=f((0-x)/(1-0))=f(-x)
∴f(x)为奇函数
(2)
∵f(xn)+f(xn)=f(xn)-f(-xn)=f((xn-(-xn))/(1-xn(-xn)))=f(2xn/(1+xn²))=f(xn+1)
∴公比q=f(xn+1)/f(xn)=2,
首项a1=f(x1)=f(1/2)=1,
∴{f(xn)}是首项为1,公比为2的等比数列
通项an=f(xn)=2^(n-1)
(3)
Tn=Σ(2n-1)/2^(n-1)=1+3/2+5/2^2+...+(2n-1)1/2^(n-1)
Tn/2=1/2+3/2^2+5/2^3+...+(2n-1)/2^(n)
两式相减:
Tn/2=1+(3/2-1/2)+(5/2^2-3/2^2)+...+((2n-1)1/2^(n-1)-(2n-3)1/2^(n-1))-(2n-1)/2^(n)
=1+2[1/2+1/2^2+1/2^3+...+1/2^(n-1)]-(2n-1)/2^(n)
=1+2(1/2(1-1/2^(n-2))/(1-1/2)-(2n-1)/2^n
=1+2-1/2^(n-1)-(2n-1)/2^n
Tn=6-(1+2n)/2^(n-1)
limTn=6
(6-3m)/2>=6
m