(1/2+1/3…+1/2003)(1+1/2+1/3+…+1/2004)-(1+1/2+1/3+…+1/2003)(1/2+1/3+…+1/2004)=?

问题描述:

(1/2+1/3…+1/2003)(1+1/2+1/3+…+1/2004)-(1+1/2+1/3+…+1/2003)(1/2+1/3+…+1/2004)=?

设a=(1/2+1/3+...+1/2003) 原式=a(1+a+1/2004)-(1+a)(a+1/2004) =a+a^2+a/2004-a-1/2004-a^2-a/2004 =-1/2004