作业帮（-1x1/2）+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/20 01:32:30
（-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）
=-｛（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
=-｛（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
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