An为等差数列,且满足A(n+1)=An²-nAn+1,n=1,2,3……求An的通项公式

a(n+1)=an^2-nan+1an=a(n-1)^2-(n-1)a(n-1)+1两式相减d=(2a(n-1)+d)*d-nd-a(n-1)d=2a1d+d^2-2d-a1d=2a2d+d^2-3d-a2两式相减2d^2-d-d=0得d1=0,d2=1当d=0时 解得a1=1 an=1当d=1时 解得a1=0或2当a1=0时 an=n-1 代入式An...