an＝2sn方 2sn-1,

答案为ASn=((a1+an)/2)*nan=a1+(n-1)d根据上式得出：Sn=(2a1+(n-1)d)*n/2=a1*n+n方*d/2-n*d/2limSn/n方=lim(2a1*n+n方*d-

当n=1时、有2s1+1=3a1,即有a1=1,因为2Sn+1=3an,所以2Sn+1+1=3an+1.后式减去前式,得2an+1=3an+1-3an.即有an+1=3an,为等比数列,且公比为3,所

an+2Sn*Sn-1=0其中an=Sn-Sn-1代入上式：Sn-Sn-1+2Sn*Sn-1=0a1＝1/2,故Sn和Sn-1≠0,上式两边同除以Sn*Sn-1得：1/Sn-1-1/Sn+2＝0即：1

由Sn=Sn-1/2Sn-1+1,两边同时取倒数可得1/Sn=(2Sn-1+1)/Sn-11/Sn=2+1/Sn-1即1/Sn-1/Sn-1=2故{1/Sn}是首项为1/2,公差为2的等差数列1/Sn

an=-Sn.S(n-1)Sn-S(n-1)=-Sn.S(n-1)1/Sn-1/S(n-1)=11/Sn-1/S1=n-11/Sn=nSn=1/n

n>=2时,Sn^2=(Sn-S(n-1))(Sn-1/2)化简得0=-SnS(n-1)-(1/2)Sn+(1/2)S(n-1).即1/Sn-1/S(n-1)=2所以1/Sn是以2为公差的等差数列.首

sn=2n^2-n+2s(n-1)=2(n-1)^2-(n-1)+2两式相减an=4n-3

A1=6;n>1时,an=Sn-S(n-1)=6n-1.

(1)设Sn-S(n-1)=an原式可化为1/2[Sn-S(n-1)]=-Sn*S(n-1)两边同除-1/2*Sn*S(n-1),可得1/Sn-1/S(n-1)=2设cn=1/Sn,可得当n>或=2时

我会我会Sn+1=Sn-2nSn+1Sn两边同除以Sn+1*Sn得1/Sn+1-1/Sn=2n以此类推1/Sn-1/Sn-1=2(n-1)1/Sn-1-1/Sn-2=2(n-2)...1/S2-1/S

由题意,S(n)-S(n-1)=2a(n+1)-2a(n),即a(n)=2a(n+1)-2a(n),于是a(n+1)=a(n)*3/2,即a(n)是公比是q=3/2的等比数列,且首项是a(1)=1,所

n>=2时：∵an=2Sn^2/[（2Sn）-1]∴Sn-(Sn-1)=2Sn^2/[（2Sn）-1]两边同时乘以（2Sn）-1并化简得2Sn(Sn-1)+Sn-(Sn-1)=0两边同时除以Sn(Sn

n≥2时,an=Sn-S(n-1)=2Sn²/(2Sn-1)[Sn-S(n-1)](2Sn-1)=2Sn²-Sn-2SnS(n-1)+S(n-1)=0S(n-1)-Sn=2SnS(

1）设an=a1*q^(n-1),则有Sn=a1*(1-q^n)/(1-q),[Sn*Sn+2-（Sn+1）^2]=a1^2*{(1-q^n)*[1-q^(n+2)]-[1-q^(n+1)]^2}/(

因为Sn+Sn-1=3an所以Sn-1+Sn-1+an=3an2Sn-1=2anSn-1=an因为Sn=an+1所以Sn-Sn-1=an+1-anan=an+1-an2an=an+1an+1/an=2

Sn-1=(n-1)(n-1)an-1Sn-Sn-1=an=nnan-(n-1)(n-1)an-1(nn-1)an=(n-1)(n-1)an-1an=(n-1)/(n+1)*(n-2)/(n-1)*…

Sn=n^2+2n-1,S1=1^2+2-1=2an=Sn-S(n-1)=n^2+2n-1-[(n-1)^2+2(n-1)-1]=2n+1a1=3所以a1≠S1当n=1时an=2当n>1时an=2n+

2(Sn+1)(Sn)/(Sn-Sn+1)=1上下除以(Sn+1)(Sn)得到2/(1/Sn+1-1/Sn)=11/(Sn+1)-1/Sn=2因此1/Sn+1为等差数列,1/S1=1/a1=1/21/

已知Sn=2An-1取n=1得:S1=2A1-1又因为S1=A1,解上述方程可得:A1=1Sn=2An-1S(n-1)=2A(n-1)-1注:"n-1"为下标上下两式相减得:Sn-S(n-1)=2An

证明如下：