已知数列{an}是首项为1的正项数列,且（n+1)*a(n+1)^2-n*an^2+a(n+1)an=0,则它的通项公式an=_________.

已知数列{an}是首项为1的正项数列,且（n+1)*a(n+1)^2-n*an^2+a(n+1)an=0,则它的通项公式an=_________.
已知数列{an}是首项为1的正项数列,且（n+1)*a(n+1)^2-n*an^2+a(n+1)an=0,则它的通项公式an=_________.

已知数列{an}是首项为1的正项数列,且（n+1)*a(n+1)^2-n*an^2+a(n+1)an=0,则它的通项公式an=_________.
（n+1)*a(n+1)^2-n*an^2+a(n+1)an=0
==> [(n+1)a(n+1)-n*an]*[a(n+1)+an]=0
已知是正项数列
==> (n+1) * a(n+1)= n * an
可知数列{n*an} 是 以 {1 * a1}为首项,公比为 1 的等比数列
==> n * an = (1*a1) * 1^(n-1)
==> an = 1/n

n[a(n+1)^2-an^2]-nan^2+a(n+1)an=0
n[a(n+1)-an](a(n+1)+an)+[a(n+1)+an]+a(n+1)=0
[na(n+1)-nan+a(n+1)][a(n+1)+an]=0
所以通项公式为
a(n+1)=-an或a(n+1)=[n/(n+1)]an