(n+1)*a(n+1)^2-n*an^2+an*a(n+1)=0n*(a(n+1)^2-an^2)+a(n+1)^2+an*a(n+1)=0(a(n+1)+an)((n+1)*a(n+1)-n*an)=0又{an}为正项数列,(n+1)*a(n+1)-n*an=0(n+1)*a(n+1)=n*an1*a1=1an=1/n