1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/18 11:43:50
1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+
1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)
1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)
1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)
1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)
=1/(x-1)+1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+.+1/(x-100)-1/(x-99)
=1/(x-100)
原式=1/(x-1)+1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+1/(x-4)-1/(x-3)+...+1/(x-100)-1/(x-99)
中间正负抵消
=1/(x-100)
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