已知a1+a2+……+an=n×n×n,求：1/（a2-1）+1/（a3-1）+1/（a4-1）+……+1/（a2011

∵a1+a2+……+an=n×n×n
∴an=n^3-(n-1)^3=n^2+n*(n+1)+(n+1)^2=n^2+(n^2+n)+(n^2+2n+1)=3n^2+3n+1
1/（an-1）=1/（3n^2+3n+1-1）=1/(3n*(n+1))=1/3*[1/n - 1/(n+1)]
1/（a2-1）+1/（a3-1）+1/（a4-1）+……+1/（a2011-1）
=1/3*{(1/2 - 1/3)+(1/3 - 1/4)+(1/4 - 1/5)+……(1/2011 - 1/2012)}
=1/3*(1/2 - 1/2012)
=1/3*(2012-2)/(2012*2)
=335/2012