1/1+1/2+2/2+1/2······1/2012+2/2012+······2012/2012+······2/2012+1/2012=====

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/09 13:37:49
1/1+1/2+2/2+1/2······1/2012+2/2012+······2012/2012+······2/2012+1/2012=====

1/1+1/2+2/2+1/2······1/2012+2/2012+······2012/2012+······2/2012+1/2012=====
1/1+1/2+2/2+1/2······1/2012+2/2012+······2012/2012+······2/2012+1/2012
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1/1+1/2+2/2+1/2······1/2012+2/2012+······2012/2012+······2/2012+1/2012=====
楼主:
1/1+1/2+2/2+1/2······1/2012+2/2012+······2012/2012+······2/2012+1/2012
=2/2+3/2+4/2+……+2013/2
=1/2×(2+3+4+……+2013)
=1/2×(2+2013)×2012/2
=2015×503
最后=1013545

1/1+1/2+2/2+1/3+2/3+3/3.......+1/2012+2/2012...+2012/2012
=2/2+3/2+4/2+……+2013/2
=1/2×(2+3+4+……+2013)
=1/2×(2+2013)×2012/2
=2015×503
=1013545

原式=2/2+3/2+4/2+……+2013/2
=1/2×(2+3+4+……+2013)

=1/2×(2+2013)×2012/2
=2015×503

=1013545

1+2+…… +n+……+2+1=n^2
(1+2+…… +n+……+2+1)/n=n
∴原式=1+2+3+…… +2012=(1+2012)*2012/2=2025078

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