已知对于任意正整数n,有a1+a2+a3...+an=n^3,求(1/a2-1)+(1/a3-1)+...+(1/a10

an=n^3-(n-1)^3=3n^2-3n+1
an-1=3n^2-3n=3n(n-1)
1/(an-1)=[1/(n-1)-1/n]/3
1/(a2-1)+1/(a3-1)+...+1/(a100-1)=[(1/1-1/2)+(1/2-1/3)+...+(1/99-1/100)]/3=(1-1/100)/3=33/100