设f(x)=4^x/4^x+2,那么f(1/11)+f(2/11)+f(3/11)+…………+f(10/11)的值为?

设函数f(x)=4^x/(4^x+2)
则f(x)+f(1-x)=4^x/(4^x+2)+4^(1-x)/[4^(1-x)+2]
=4^x/(4^x+1)+4/(4+2*4^x]
=4^x/(4^x+2)+2/(4^x+2)
=(4^x+2)/(4^x+2)
=1 (注意：f(x)+f(1-x)=1 其中x+1-x=1)
所以f(1/11)+f(2/11)+……+f(10/11)
=[f(1/11)+f(10/11)]+[f(2/11)+f(9/11)]+...+[f(5/11)+f(6/11)]
=1+1+1+1+1
=5