(1/2001-1/2002)-(1/2003-1/2002)-(1/2001-1/2003)
=1/2001-1/2002-1/2003+1/2002-1/2001+1/2003
=(1/2001-1/2001)+(1/2002-1/2002)+(1/2003-1/2003)
=0+0+0
0