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化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2013)(x+2014)

分类: 作业答案 • 2021-11-12 22:48:31
问题描述：

化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2013)(x+2014)

答

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2013)(x+2014)=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+2013)-1/(x+2014)=1/x-1/(x+2014)=2014/x(x+2014)

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