已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).求数列{an}的已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).(1)求数列{an}
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![已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).求数列{an}的已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).(1)求数列{an}](/uploads/image/z/8508200-32-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%E6%BB%A1%E8%B6%B3%EF%BC%9ASn%3Da%2Fa-1%EF%BC%88an-1%29%28a%E4%B8%BA%E5%B8%B8%E6%95%B0%2C%E4%B8%94a%E4%B8%8D%E7%AD%89%E4%BA%8E0%2Ca%E4%B8%8D%E7%AD%89%E4%BA%8E1%EF%BC%89.%E6%B1%82%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%E6%BB%A1%E8%B6%B3%EF%BC%9ASn%3Da%2Fa-1%EF%BC%88an-1%29%28a%E4%B8%BA%E5%B8%B8%E6%95%B0%2C%E4%B8%94a%E4%B8%8D%E7%AD%89%E4%BA%8E0%2Ca%E4%B8%8D%E7%AD%89%E4%BA%8E1%EF%BC%89.%EF%BC%881%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D)
已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).求数列{an}的已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).(1)求数列{an}
已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).求数列{an}的
已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).(1)求数列{an}的通项公式;(2)设bn=2Sn/an+1,若{bn}为等比数列,求a的值;(3)在满足(2)的情形下,设cn=1/1+an+1/1-an+1,数列{cn}的前n项和为Tn,求证:Tn大于2n-1/3
尤其是第3问
已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).求数列{an}的已知数列{an}的前n项和Sn满足:Sn=a/a-1(an-1)(a为常数,且a不等于0,a不等于1).(1)求数列{an}
答:n=1时,a[1]=s[1]=a/(a-1)(a[1]-1),a[1]=a;
a[n+1]=s[n+1]-s[n]=a/(a-1)*(a[n+1]-a[n]),解得:a[n+1]=aa[n],故a[n]=a[1]a^(n-1)=a^n
(2)将a[n]=a^n代入b[n]=(2S[n]/a[n])+1中得:b[n]=(3a-2a^(1-n)-1)/(a-1),若数列{bn}为等比数列,
则b[1],b[2],b[3]必成等比列,由此可推出:a=1/3;
(3)c[n]=1/{1+(1/3)^n}+1/{1-(1/3)^(n+1)}=3^n/(1+3^n)+3^(n+1)/(3^(n+1)-1)=2+1/{3^(n+1)-1}-1/(1+3^n)>2-{1/3^n-1/3^(n+1)}
故T[n]>2n-{1/3-1/3^(n+1)}>2n-1/3
Sn=a/a-1(an-1)
看不懂啊