1/n(n+1)=1/n-1/(n+1)1/1*2+1/2*3+1/3*4+1/4*5...+1/2002*2003+1/2003*2004+1/2004*2005=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2003-1/2004+1/2004-1/2005=1-1/2005=2004/2005