设x=1/2+1/3+...+1/2003
y=1/2+1/3+...+1/2002
（1/2+1/3+...+1/2003)(1+1/2+...+1/2002)-(1+1/2+...+1/2003)(1/2+1/3+...+1/2002)
=x(1+y)-(1+x)y
=x+xy-y-xy
=x-y
=1/2003