1 -+*- 2*+-+
由题意可得2003-2003*1/2-2003*(1/2*1/3)-2003*(1/3*1/4)-.-2003*(1/2001*1/2002)-2003*(1/2002*1/2003),变形得2003*(1-1/2-1/2*1/3-1/3*1/4-.-1/2001*1/2002-1/2002*1/2003),在变形得,2003*(1-1/2-1/2+1/3-1/3+1/4.-1/2001+1/2002-1/2002+1/2003),计算得
2003*(1/2003)=1