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(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1

来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/11/19 17:02:34
(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1/2009)
(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1
(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1/2009)
=-{(1x1/2)+(1/2x1/3)+(1/3x1/4)+.+(1/2007x1/2008)+(1/2008X1/2009)}
=-{1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008+1/2008-1/2009}
=-(1-1/2009)
=-2008/2009
补充:1/n*1/(n+1)=1/n-1/(n+1) 例如1/2*1/3=1/2-1/3=1/6