分母和=n(n+1)/2
1/(n(n+1)/2)=2/(n(n+1))=2(1/n-1/(n+1))
1/(1+2)+1/(1+2+3)+.+1/1+2+...2012
=2*(1/2-1/3)+2*(1/3-1/4)+.+2*(1/2012-1/2013)
=2*(1/2-1/2013)
=2011/2013
预初等差数列计算
分母和=n(n+1)/2
1/(n(n+1)/2)=2/(n(n+1))=2(1/n-1/(n+1))
1/(1+2)+1/(1+2+3)+.+1/1+2+...2012
=2*(1/2-1/3)+2*(1/3-1/4)+.+2*(1/2012-1/2013)
=2*(1/2-1/2013)
=2011/2013