计算1/x-1 1/(x-1)(x-2) 1/(x-2)(x-3)… 1/(x-99)(x-100)及规律是什么

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计算1/x-1 1/(x-1)(x-2) 1/(x-2)(x-3)… 1/(x-99)(x-100)及规律是什么
计算1/x-1 1/(x-1)(x-2) 1/(x-2)(x-3)… 1/(x-99)(x-100)及规律是什么

计算1/x-1 1/(x-1)(x-2) 1/(x-2)(x-3)… 1/(x-99)(x-100)及规律是什么
原式=1/(X-1)-1/(X-2)+1/(X-2)-1/（X-3）+…+1/（X-99）-1/（X-100）
=1/(x-1） - 1/(x-100)
=(x-100)-(x-1)/(x-1)(x-100)
=-99/(x-1)(x-100)

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