Question

an^2lg(n+2)+ana（n+1）lg(n+2)/(n+1)-a（n+1）^2lg(n+1)=0,a1=1则a3=

Answer 1

a3=lg4

由an^2lg(n+2)+ana（n+1）lg(n+2)/(n+1)-a（n+1）^2lg(n+1)=0,移项后得（an+an+1)anlg(n+2)=（an+an+1)an+1lg(n+1),化简后得,a(n+1)/an=lg(n+2)/lg(n+1),

所以通项是an=1(n=1)或lg(n+1)(n>1)

代入n=3,可知a3=lg4