已知f(x)=LOGaX(a>0且a不等于1),且2,f(a1),f(a2).f(an),2n+4,...成等差数列,若数列{an}的前n项和为Sn,当a>1,求LIM(Sn/an)

已知f(x)=LOGaX(a>0且a不等于1),且2,f(a1),f(a2).f(an),2n+4,...成等差数列,若数列{an}的前n项和为Sn,当a>1,求LIM(Sn/an)
已知f(x)=LOGaX(a>0且a不等于1),且2,f(a1),f(a2).f(an),2n+4,...成等差数列,若数列{an}的前n项和为Sn,当a>1,求LIM(Sn/an)

已知f(x)=LOGaX(a>0且a不等于1),且2,f(a1),f(a2).f(an),2n+4,...成等差数列,若数列{an}的前n项和为Sn,当a>1,求LIM(Sn/an)
1.求an
"2,f(a1),f(a2).f(an),2n+4,...成等差数列"
从2到2n+4共n+2项,因此（2n+4）-2=（n-1）d,其中d为公差,得d=2.所以f(an)=2n+2
2.求Sn
f(an)=2n+2以及“f(x)=LOGaX(a>0且a不等于1)”
得an=a^(2n+2)=a^2*(a^2)*n,即公比为a^2的等比数列的通项.所以Sn=(a^4)*(1-a^2n)/(1-a^2).
3.lim(Sn/an)
若a>1,lim(Sn/an)=(a^2)/(a^2-1)
若0