(1/1004-1)*(1/1005-1)*(1/1006-1).(1/2004-1)=?

问题描述:

(1/1004-1)*(1/1005-1)*(1/1006-1).(1/2004-1)=?

(1/1004-1)*(1/1005-1)*(1/1006-1)......(1/2004-1)
=(-1003/1004)*(-1004/1005)*(-1005/1006)*......*(-2003/2004)
=-1003/2004

1003/2004
每个括号里都通分

原式=[-(1003/1004)][-(1004/1005)][-(1005/1006)].[-(2003/2004)]
=-(1003/2004)
因式子共2004-1003=1001项 所以提取一个负号