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一道数学题：1/x-1+1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-99)(x-100)

分类: 作业答案 • 2021-12-19 20:37:32
问题描述：

一道数学题：1/x-1+1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-99)(x-100)

答


原式=1/(x-1)+[1/(x-2)-1/(x-1)]+[1/(x-3)-1/(x-2)]……+[1/(x-100)-1/(x-99)]
=1/(x-1)-1/(x-1)+1/(x-2)-1/(x-2)+……+1/(x-99)-1/(x-99)+1/(x-100)
=0+0+……+1/(x-100)
=1/(x-100)

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