1/(1X2)=1- 1/2 ,1/(2X3)=1/2-1/3,1/3X4=1/3-1/4,1/x(x-1)+1/(x-1)(x-2)+.+1/(x-99)(x-100)=?我就按自己写的,老师打了对...

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/13 07:51:17
1/(1X2)=1- 1/2 ,1/(2X3)=1/2-1/3,1/3X4=1/3-1/4,1/x(x-1)+1/(x-1)(x-2)+.+1/(x-99)(x-100)=?我就按自己写的,老师打了对...

1/(1X2)=1- 1/2 ,1/(2X3)=1/2-1/3,1/3X4=1/3-1/4,1/x(x-1)+1/(x-1)(x-2)+.+1/(x-99)(x-100)=?我就按自己写的,老师打了对...
1/(1X2)=1- 1/2 ,1/(2X3)=1/2-1/3,1/3X4=1/3-1/4,1/x(x-1)+1/(x-1)(x-2)+.+1/(x-99)(x-100)=?
我就按自己写的,老师打了对...

1/(1X2)=1- 1/2 ,1/(2X3)=1/2-1/3,1/3X4=1/3-1/4,1/x(x-1)+1/(x-1)(x-2)+.+1/(x-99)(x-100)=?我就按自己写的,老师打了对...
1/x(x-1)+1/(x-1)(x-2)+.+1/(x-99)(x-100)
=[(1/x-1)-1/x]+[(1/x-2)-(1/x-1)]+[(1/x-3)-(1/x-2)]+……+[(1/x-100)-(1/x-99)]
=1/(x-100) - 1/x

就是这样, 中间的项都是正负互相抵消了,很简单

我最后算出来等于 100/x(x-100)
= - 我真勤劳