设f(x)=1/(1+2^lgx)+1/(1+4^lg4)+1/(1+8^lgx),则f(x)+f(1/x)=?

f(x)= 1/(1+2^lgx) + ...;
f(1/x)= 1/(1+2^lg(1/x)) + ...= 1/(1+2^(-lgx))+ ...
f(x)+f(1/x) = 1/(1+2^lgx) + 1/(1+2^(-lgx)) + ...
= {1+2^lgx+1+2^(-lgx)}/{1+2^lgx+2^(-lgx)+2^lgx*2^(-lgx)+ ...
= (1+ 1 2^(lgx-lgx)+..
= (1+ +1)/ (1+ 1 (2^0))+ ...
= 1 + 1 + 1
=3
省略的是同理可得啊