将数列｛an}中的所有项按每一行比上一行多一项的规则排成如下数表a1a2 a3a4 a5 a6a7

将数列｛an}中的所有项按每一行比上一行多一项的规则排成如下数表a1a2 a3a4 a5 a6a7

1.Sn=bn+Sn-1=Sn²/(Sn -2)+S n-1（n>=2）Sn²-2Sn=Sn²+(S n-1)(Sn -2)2S n-1 -2Sn=SnS n-1两边除以2SnS n-1 得1/Sn-1/Sn-1=1/2（n≥2）2.由1得1/S2-1/S1=1/21/S3-1/S2=1/2……1/Sn-1/Sn-1=1/21/Sn=(n-1)/2+1=(n+1)/2Sn=2/(n+1)bn=4/(n+1)²/(2/(n+1)-2)=4/(2n+2-2(n+1)²)=-2/n(n+1)3.a94是第14行第三项则a92=b14=-2/14(14+1)=-1/105公比p=正负根号(a94/a92)=正负3第k行第一项为bk=-2/k(k+1)则第k行的和Tk=bk*(q^k-1)/(q-1)=(-2/k(k+1))(q^k-1)/(q-1)当q=3时 Tk=-(3^k-1)/k(k+1)当q=-3时Tk=((-3)^k-1)/4k(k+1) (k>=3)======以下答案可供参考======供参考答案1:1. Sn=bn+Sn-1=Sn²/(Sn -2)+S n-1（n>=2）Sn²-2Sn=Sn²+(S n-1)(Sn -2)2S n-1 -2Sn=SnS n-1两边除以2SnS n-1 得1/Sn-1/Sn-1=1/2（n≥2）2.由1得1/S2-1/S1=1/21/S3-1/S2=1/2……1/Sn-1/Sn-1=1/21/Sn=(n-1)/2+1=(n+1)/2Sn=2/(n+1)bn=4/(n+1)²/(2/(n+1)-2)=4/(2n+2-2(n+1)²)=-2/n(n+1)3.a94是第14行第三项则a92=b14=-2/14(14+1)=-1/105公比p=正负根号(a94/a92)=正负3第k行第一项为bk=-2/k(k+1)则第k行的和Tk=bk*(q^k-1)/(q-1)=(-2/k(k+1))(q^k-1)/(q-1)当q=3时 Tk=-(3^k-1)/k(k+1)当q=-3时Tk=((-3)^k-1)/4k(k+1) (k>=3)

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