有理数的计算(1)1/1x4+1/4x7+1/7x10+...+1/2008x2011+1/2011x2014

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有理数的计算(1)1/1x4+1/4x7+1/7x10+...+1/2008x2011+1/2011x2014有理数的计算(1)1/1x4+1/4x7+1/7x10+...+1/2008x2011+1

有理数的计算(1)1/1x4+1/4x7+1/7x10+...+1/2008x2011+1/2011x2014
有理数的计算
(1)1/1x4+1/4x7+1/7x10+...+1/2008x2011+1/2011x2014

有理数的计算(1)1/1x4+1/4x7+1/7x10+...+1/2008x2011+1/2011x2014
1/1x4+1/4x7+1/7x10+...+1/2008x2011+1/2011x2014
=(1-1/4+1/4-1/7+1/7-1/10+...+1/2008-1/2011+1/2011-1/2014)/3
=(1-1/2014)/3=671/2014

用列项公式前面加个1/3过程为1/3(1-1/4+1/4-1/7...+1/2011-1/2014)=1/3x(1-1/2014)=671/2014