-1/10*11-1/11*12-1/12*13-……-1/19*20

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 21:41:44
-1/10*11-1/11*12-1/12*13-……-1/19*20

-1/10*11-1/11*12-1/12*13-……-1/19*20
-1/10*11-1/11*12-1/12*13-……-1/19*20

-1/10*11-1/11*12-1/12*13-……-1/19*20
原式=-(1/10*11+1/11*12+1/12*13……+1/19*20)
=-(1/10-1/11+1/11-1/12+1/12-1/13……+1/19-1/20)
=-(1/10-1/20)
=-1/20

原式=-1*(1/10 -1/11 +1/11 -1/12 +……1/19-1/20)=-1*(1/10-1/20)=-1/20

-1/10*11-1/11*12-1/12*13-……-1/19*20
=-(1/10*11+1/11*12+1/12*13+..+1/19*20)
=-(1/10-1/11+1/11-1/12+1/12-1/13+...1/19-1/20)
=-(1/10-1/20)
=-1/20

可把1/(10*11)拆成1/10-1/11,这两个是相等的,后面同理,可一一约掉,只剩头尾

拆项相消
原式=-(1/10-1/11+1/11-1/12+1/12-1/13……+1/19-1/20)
=-(1/10-1/20)
=-1/20