在数列{an}中,a1=2,nan+1=(n+1)an+2,则a10为

在数列{an}中,a1=2,nan+1=(n+1)an+2,则a10为
在数列{an}中,a1=2,nan+1=(n+1)an+2,则a10为

在数列{an}中,a1=2,nan+1=(n+1)an+2,则a10为
na(n+1)=(n+1)an+2
n[a(n+1)+t]=(n+1)(an+t)
t=2
[a(n+1)+2]/(an+2)=(n+1)/n
(a2+2)/(a1+2)=2/1
(a3+2)/(a2+2)=3/2
(a4+2)/(a3+2)=4/3
..........
(an+2)[a(n-1)+2]=n/(n-1)
式子相乘
(an+2)/(a1+2)=n
an=4n-2
a10=38