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解方程:x-1分之1加(x-1)乘以(x-2)分之1加(x-2)乘以(x-3)分之1+……+(x-99)乘以(x-100

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/15 00:03:34
解方程:x-1分之1加(x-1)乘以(x-2)分之1加(x-2)乘以(x-3)分之1+……+(x-99)乘以(x-100)=1
题目应是x-1分之1加(x-1)乘以(x-2)分之1加(x-2)乘以(x-3)分之1+……+(x-99)乘以(x-100)分之1=1
1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+……+1/(x-99)(x-100)=1
1/(x-1)+1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+……+1/(x-100)-1/(x-99)=1
1/(x-100)=1
x-100=1
x=101