www.ypnh.net > 1*1/2+1/2*1/3+1/3*1/4……+1/2017=

1*1/2+1/2*1/3+1/3*1/4……+1/2017=

1*1/2+1/2*1/3+1/3*1/4……+1/2017*1/2018 =1-1/2+1/2-1/3+1/3-1/4+……+1/2017-1/2018 =1-1/2018 =2017/2018

1*1/2+1/2*1/3+1/3*1/4……+1/2017*1/2018 =1-1/2+1/2-1/3+1/3-1/4+……+1/2017-1/2018 =1-1/2018 =2017/2018

1+1/2×1/3+1/3×1/4+…+1/2016*1/2017 =1+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2016-1/2017 =1+1/2-1/2017 =4034/4034+2017/4034-2/4034 =6049/4034

|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+...+|1/2016-1/2017| =1/2-1/3+1/3-1/4+1/4-1/5+……+1/2016-1/2017 =1/2-1/2017 =2015/4034

解: 以1为分母的数字,共有1个; 以2为分母的数字,共有1个; 以3为分母的数字,共有2个; 以4为分母的数字,共有3个; …… 以n为分母的数字,共有n个。 由1+1+2+3+……+n=2017,可以解得n=63。(很完美。) 也就是说,第2017个数刚好是以63为分母...

约等于: 8.186830075

=1009/2019

1/2+1/2*3+1/3*4+...+1/2016*2017 =1/2+(1/2-1/3)+(1/3-1/4)+...(1/2016-1/2017) =1/2+1/2-1/3+1/3-1/4+...1/2016-1/2017 =1/2+1/2-1/2017 =2016/2017

1/(1×2)-1/(2×3)-1/(3×4)-……-1/(2017×2018) =(1/1-1/2)-(1/2-1/3)-(1/3-1/4)-......-(1/2017-1/2018) =1/1-1/2-1/2+1/3-1/3+1/4-1/4+1/5-...-1/2016+1/2017-1/2017+1/2018 =1/2018

1+2+...+n=n(n+1)/2 所以1/(1+2+...+n)=2/n(n+1)=2[1/n-1/(n+1)] x+x/(1+2)+x/(1+2+3)…+x/(1+2+3+…+2017)=2017 2x[(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2017-1/2018)]=2017 2x(1-1/2018)=2017 2017x/1009=2017 x=1009×2017/2017 x=1009

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