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化简1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+2009)(x+2010并且当x=1时,该

分类: 作业答案 • 2021-12-20 01:28:22
问题描述：

化简1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+2009)(x+2010并且当x=1时,该

答

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1(x+2009)(x+2010)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2009)-1/(x+2010)
=1/x-1/(x+2010)
故当x=1时,原式=1 -1/2011 =2010/2011

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