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1/(a-1)+1/(a-1)(a-2)+1(a-2)(a-3).1/(a-99)(a-100)

分类: 作业答案 • 2021-12-19 23:44:45
问题描述：

1/(a-1)+1/(a-1)(a-2)+1(a-2)(a-3).1/(a-99)(a-100)

答

1/n(n-1)=1/(n-1)-1/n
题目=1/(a-1)+1/(a-2)-1/(a-1)+...+1/(a-100)-1/(a-99)=1/(a-100)

答

1/(a-100)

答

1/(a-1)+1/(a-1)(a-2)+1(a-2)(a-3).1/(a-99)(a-100)
=1/(a-1)+1/(a-1)-1/(a-2)+1/(a-2)-1/(a-3)+.+1/(a-99)-1/(a-100)
=2/(a-1)-1/(a-100)
=[2(a-100)-2]/(a-1)(a-100)
=(2a-202)/(a-1)(a-100)

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