已知An(an,bn)是曲线y=e^x上的点,a1=a,Sn是数列{an}的前n项和,且满足Sn^2=(3n^2)an+S(n-1)^2已知An(an,bn)是曲线y=e^x上的点,a1=a,Sn是数列{an}的前n项和,且满足Sn^2=3n^2*an+S(n-1)^2,an不等于0,n=2,3,4…(1)证明：数列{

问题：已知An(an,bn)是曲线y=e^x上的点,a1=a,Sn是数列{an}的前n项和,且满足Sn^2=(3n^2)an+S(n-1)^2已知An(an,bn)是曲线y=e^x上的点,a1=a,Sn是数列{an}的前n项和,且满足Sn^2=3n^2*an+S(n-1)^2,an不等于0,n=2,3,4…(1)证明：数列{

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陈彦萼的回答：

网友采纳　　(1)证明：b(n+2)/bn=e^a(n+2)/e^an=e^[a(n+2)-an]要证明{b(n+2)/bn}为常数数列,只需证a(n+2)-an为常数；∵Sn^2=3n^2*an+S(n-1)^2∴Sn^2-S(n-1)^2=[Sn+S(n-1)][Sn-S(n-1)]=[Sn+S(n-1)]*an=3n^2*an∴Sn+S(n-1)=3n^2…...