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1/x(x+2)+1/(x+2)*(x+4)+1/(x+4)*(x+6)+.+1/(x+2000)*(x+2002)

分类: 作业答案 • 2022-04-29 09:23:57
问题描述：

1/x(x+2)+1/(x+2)*(x+4)+1/(x+4)*(x+6)+.+1/(x+2000)*(x+2002)

答

1/x(x+2)+1/(x+2)*(x+4)+1/(x+4)*(x+6)+.+1/(x+2000)*(x+2002)=1/2(1/x-1/(x+2))+1/2(1/(x+2)-1/(x+4))+1/2(1/(x+4)-1/(x+6))+.+1/2(1/(x+2000)-1/(x+2002))=1/2(1/x-1/(x+2002))=1/2(2002/x(x+2002))=1001/x(x+2002...

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