数列an中,已知a1=6,nan-na【(n-1)】下标=a(n-1)+n方+n(n>=2) 1设bn=an/(n+1)求证bn是等比数列2,求

问题描述:

数列an中,已知a1=6,nan-na【(n-1)】下标=a(n-1)+n方+n(n>=2) 1设bn=an/(n+1)求证bn是等比数列2,求
数列an的通项公式

nan﹣nan-1=an-1+n²+n
nan=(n+1)an-1+n²+n
同除n²+n
则an/(n+1)=(an-1/n) +1
∴an/(n+1)=n+2
an=(n+1)(n+2)