设f(x)=4^x/(4^x+2)求f(1/1001)+f(2/1001)+……+f(1000/1001)的值

问题描述:

设f(x)=4^x/(4^x+2)求f(1/1001)+f(2/1001)+……+f(1000/1001)的值

f(x)+f(1-x)=4^x/(4^x+2)+4^(1-x)/[4^(1-x)+2]=4^x/(4^x+2)+(4/4^x)/[(4/4^x)+2]=4^x/(4^x+2)+4/(4+2*4^x)=4^x/(4^x+2)+2/(2+4^x)=(4^x+2)/(4^x+2)=1所以f(1/1001)+f(2/1001)+……+f(1000/1001)=[f(1/1001)+f(1000/1...