a.1/1.2+1/2.3+1/3.4+...+1/2003.2004
=1/1-1/2+1/2-1/3+1/3-1/4+....+1/2003-1/2004
=1-1/2004
=2004/2004-1/2004
=2003/2004
b,1/1.3+1/3.5+1/5.7+....+1/2003.2005
=1.3/3.1.3+1.3/3.3.5+1.3/3.5.7+...+1.3/3.2003.2005
=1/3(3/1.3+3/3.5+3/5.7+....+3/2003.2005)
=1/3(1/1-1/3+1/3-1/5+1/5-1/7+.....+1/2003-1/2005)
=1/3(1-1/2005)
=1/3(2005/2005-1/2005)
=1/3.2004/2005
=1.2004/3.2005
=1.668/1.2005
=668/2005