已知f(x)=1+x分之x求f(1/2004)+f(1/2003)+~+f(1/1)+f(0/1)+f(1/1)~f(2004/1)的值?

问题描述:

已知f(x)=1+x分之x求f(1/2004)+f(1/2003)+~+f(1/1)+f(0/1)+f(1/1)~f(2004/1)的值?

f(x)+f(1/x)=x/(1+x)+(1/x)/(1+1/x)=x/(1+x)+1/(x+1)=(x+1)/(x+1)=1f(1/2004)+f(1/2003)+~+f(1/1)+f(0/1)+f(1/1)~f(2004/1)=[f(1/2004)+f(2004/1)]+[f(1/2003)+f(2003/1)]+[f(1/2002)+f(2002/1)]+……+[f(1/1)+f(...