{1\2005-1/2004}+{1/2004-1\2003}+{1/2003-1/2002}+……+{1/3-1/2}+{1/2-1}
=1/2005+(-1/2004+1/2004)+(-1/2003+1/2003)+...+(-1/2+1/2)-1
=1/2005-1
=-2004/2005