(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+...+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670)=

来源：学生作业帮助网编辑：作业帮时间：2024/05/13 07:30:45

(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+...+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670)=
(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+...+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670)=

(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+...+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670)=
=(1/4+...+1/670 + 1/671) (1/3+...+1/670) - (1/3+ ...+ 1/670 + 1/671) (1/4+ ...+1/670)
=(1/4+...+1/670) * (1/3+...+1/670) + 1/671* (1/3+...+1/670) - (1/3+ ...+1/670) * (1/4+ ...+1/670) - 1/671*(1/4+ ...+1/670)
=1/671* (1/3+...+1/670) - 1/671*(1/4+ ...+1/670)
=1/671 * (1/3 + ...1/670 - (1/4+ ...+1/670))
=1/671 * (1/3-1/4)
=1/(671*12)
=1/8052