学帮网计算:1/x(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-19)(x-20)
来源：学生作业学帮网 编辑：学帮网 时间：2024/05/18 10:36:48
计算:1/x(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-19)(x-20)
1/x(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-19)(x-20)
=[1/(x-1)-1/x]+[1/(x-2)-1/(x-1)]+[1/(x-3)-1/(x-2)]+.+[1/(x-20) -1/(x-19) ]
=1/(x-20)-1/x
原式=1/(x-1)-1/x+1/(x-2)-1/(x-1)+……+1/(x-20)-1/(x-19*)
=1/(x-20)-1/x
=20/x(x-20)
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