1△2＋2△3＋3△4＋...＋2004△2005
=(2-1)/(2*1)+(3-2)/(3*2)+(4-3)/(4*3)+...+(2005-2004)/(2005*2004)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2004-1/2005
=1-1/2005
=2004/2005