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1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2007)

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/22 09:58:35
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2007)
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2007)
=2/1*2 +2/2*3 +2/3*4 +2/4*5 +……+2/2007*2008
=2*(1/1-1/2 +1/2 -1/3+1/3-1/4+1/4-1/5+……+1/2007-1/2008)
=2*(1-1/2008)
=4014/2008
=2007/1004