m/(1×2)+m/(2×3)+m/(3×4)+...+m/(2003×2004)+m/(2004×2005)=m[1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2003×2004)+1/(2004×2005)]=m(1-1/2+1/2-1/3+1/3-1/4+...+1/2003-1/2004+1/2004-1/2005)=m(1-1/2005)=2004m/...