1/2+(1/3+2/3)+(1/4+2/4+3/4)+…(1/2006+2/2006+3/2006+…+2005/2006)=?1/2+〔1/3+2/3〕+〔1/4+2/4+3/4〕+…+〔1/2006+2/2006+…+2004/2006+2005/2006〕=0.5+1+1.5+.1003=2006*(0.5+1003)/2=1006510.
来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 05:02:31
1/2+(1/3+2/3)+(1/4+2/4+3/4)+…(1/2006+2/2006+3/2006+…+2005/2006)=?1/2+〔1/3+2/3〕+〔1/4+2/4+3/4〕+…+〔1/2006+2/2006+…+2004/2006+2005/2006〕=0.5+1+1.5+.1003=2006*(0.5+1003)/2=1006510.
1/2+(1/3+2/3)+(1/4+2/4+3/4)+…(1/2006+2/2006+3/2006+…+2005/2006)=?
1/2+〔1/3+2/3〕+〔1/4+2/4+3/4〕+…+〔1/2006+2/2006+…+2004/2006+2005/2006〕
=0.5+1+1.5+.1003
=2006*(0.5+1003)/2
=1006510.
1/2+(1/3+2/3)+(1/4+2/4+3/4)+…(1/2006+2/2006+3/2006+…+2005/2006)=?1/2+〔1/3+2/3〕+〔1/4+2/4+3/4〕+…+〔1/2006+2/2006+…+2004/2006+2005/2006〕=0.5+1+1.5+.1003=2006*(0.5+1003)/2=1006510.
分组:
(1/2),(1/3,2/3),(1/4,2/4,3/4),……
每一组的分母为组号+1,分子从1到组号,第n组的和为
1/(n+1)+2/(n+1)+...+n/(n+1)=(1+2+...+n)/(n+1)=[n(n+1)/2]/(n+1)=n/2
1/2+(1/3+2/3)+(1/4+2/4+3/4)+…(1/2006+2/2006+3/2006+…+2005/2006)
=(1+2+...+2005)/2
=2005×2006/2
=2011015