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

分类: 作业答案 • 2021-12-23 10:16:42

问题描述：

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)

答

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)