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计算1/x(x+2)+1/(x+2)(x+4)+1/(x+4)(x+6)+...1/(x+2004)(x+2006)

分类: 作业答案 • 2021-11-30 10:19:46
问题描述：

计算1/x(x+2)+1/(x+2)(x+4)+1/(x+4)(x+6)+...1/(x+2004)(x+2006)

答

1/x(x+2)+1/(x+2)(x+4)+1/(x+4)(x+6)+...1/(x+2004)(x+2006)
=1/x(x+2)+{1/(x+2)-1/(x+4)+1/(x+4)-1/(1+6)+...+1/(x+2004)-1/(x+2006)}/2
=1/x-1/(x+2)+{1/(x+2)-1/(x+2006)}/2
=1/x-1/(2x+4)-1/(2x+4012)

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