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1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)

分类: 作业答案 • 2021-12-03 14:24:36
问题描述：

1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)

答

1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)
=1/(x-1)+1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+.+1/(x-100)-1/(x-99)
=1/(x-100)请问怎么得到第一步?1/(x-1)(x-2)
=[(x-1)-(x-2)]/(x-1)(x-2)
=(x-1)/(x-1)(x-2)-(x-2)/(x-1)(x-2)
=1/(x-2)-1/(x-1)
后面的同理可得

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