2*3分之1+3*4分之1+4*5分之1、、、+2001*2002分之1+2002*2003分之1
=1/2-1/3+1/3-1/4+1/4-1/5+.+1/2001-1/2002+1/2002-1/2003
=1/2-1/2003
=2003/4006-2/4006
=2001/4006