设m=1/2+1/3+...+1/2002原式=m*(1+m-1/2002)-(1+m)(m-1/2002)=m*(m+2001/2002)-(m+1)(m-1/2002)=m^2+2001m/2002-m^2-m+m/2002+1/2002=(2001+1)m/2002-m+1/2002=m-m+1/2002=1/2002