数列An中,a1=3,nAn+1=(n+2)An,求通项an,

数列An中,a1=3,nAn+1=(n+2)An,求通项an,
数列An中,a1=3,nAn+1=(n+2)An,求通项an,

数列An中,a1=3,nAn+1=(n+2)An,求通项an,
用累积法做,
由A(n+1)/An=(n+2)/n
得
A(n)/A（n-1)=(n+1)/n-1
A(n-1)/A(n-2)=n/n-2
A(n-2)/A(n-3)=n-1/n-3
A(n-3)/A(n-4)=n-2/n-4
A(n-4)/A(n-5)=n-3/n-5
A(n-5)/A(n-6)=n-4/n-6
……
A3/A2=4/2
A2/A1=3/1
上式左乘左=右乘右
最后得,An/A1=(n+1)n/2
即An=3(n+1)n/2
将n=1代入得,A1=3,说明A1也满足,
故,通项公式为An=3(n+1)n/2