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1/x(x+1)(x+2)+1/(x+1)(x+2)(x+3).+1/(x+98)(x+99)(x+100)=?

分类: 作业答案 • 2021-11-13 00:31:41
问题描述：

1/x(x+1)(x+2)+1/(x+1)(x+2)(x+3).+1/(x+98)(x+99)(x+100)=?

答

1/x(x+1)(x+2)+1/(x+1)(x+2)(x+3).+1/(x+98)(x+99)(x+100)=(1/2){[1/x(x+1) - 1/(x+1)(x+2)] + [1/(x+1)(x+2) - 1/(x+2)(x+3)]+.+[1/(x+98)(x+99) - 1/(x+99)(x+100)]}=(1/2){1/x(x+1) - 1/(x+99)(x+100)}=[(x+99)(x...

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