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计算1/（x-1)+1/（（x-1)(x-2))+1/((x-2)(x-3))+.+1/((x-99)(x-100))

来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/16 14:00:54
计算1/（x-1)+1/（（x-1)(x-2))+1/((x-2)(x-3))+.+1/((x-99)(x-100))
答案是1/(x-100)
计算1/（x-1)+1/（（x-1)(x-2))+1/((x-2)(x-3))+.+1/((x-99)(x-100))
1/[(x-1)(x-2)]=1/(x-2)-1/(x-1).
依此类推,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-100)
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