设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3…)(1)求q的取值范围?设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3,4,5……)(1) 求q的取值范围?(2) 设bn=a(n+2)-(3/2)a(n+1),设{bn}的前n项和为Tn,比
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![设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3…)(1)求q的取值范围?设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3,4,5……)(1) 求q的取值范围?(2) 设bn=a(n+2)-(3/2)a(n+1),设{bn}的前n项和为Tn,比](/uploads/image/z/7293790-46-0.jpg?t=%E8%AE%BE%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E5%85%AC%E6%AF%94%E4%B8%BAq%2C%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%3E0%EF%BC%88n%EF%BC%9D1%2C2%2C3%E2%80%A6%EF%BC%89%281%29%E6%B1%82q%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%3F%E8%AE%BE%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E5%85%AC%E6%AF%94%E4%B8%BAq%2C%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%3E0%EF%BC%88n%EF%BC%9D1%2C2%2C3%2C4%2C5%E2%80%A6%E2%80%A6%EF%BC%89%EF%BC%881%EF%BC%89+%E6%B1%82q%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%3F%282%EF%BC%89+%E8%AE%BEbn%3Da%28n%2B2%29-%283%2F2%29a%28n%2B1%29%2C%E8%AE%BE%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BATn%2C%E6%AF%94)
设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3…)(1)求q的取值范围?设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3,4,5……)(1) 求q的取值范围?(2) 设bn=a(n+2)-(3/2)a(n+1),设{bn}的前n项和为Tn,比
设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3…)(1)求q的取值范围?
设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3,4,5……)(1) 求q的取值范围?(2) 设bn=a(n+2)-(3/2)a(n+1),设{bn}的前n项和为Tn,比较Sn/Tn?
希望给出详细解答,谢谢!
设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3…)(1)求q的取值范围?设等比数列{an}公比为q,前n项和Sn>0(n=1,2,3,4,5……)(1) 求q的取值范围?(2) 设bn=a(n+2)-(3/2)a(n+1),设{bn}的前n项和为Tn,比
1)设等比数列通式an=a1q^(n-1)
显然a1大于零 【否则s10 所以00
2)bn=a(n+2)-(3/2)*a(n+1)=a(n)*q^2-(3/2)*a(n)*q
=a*[q^2-(3/2)*q]
所以Tn=Sn*[q^2-(3/2)*q
因为q>0
若q^2-(3/2)*q>1 即q>2时 Tn>Sn
若q^2-(3/2)*q=1 即q=2时 Tn=Sn
若q^2-(3/2)*q
【【【【解答】】】】(1)因为{an}是等比数列,Sn>0,可得a1=S1>0,q≠0.当q=1时,Sn=na1>0. 当q≠1时,Sn=qqan−−1)1(1>0,即qqn−−11>0 (n=1,2,…),上式等价于不等式组 )1(01,01<−<−nqq或...
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【【【【解答】】】】(1)因为{an}是等比数列,Sn>0,可得a1=S1>0,q≠0.当q=1时,Sn=na1>0. 当q≠1时,Sn=qqan−−1)1(1>0,即qqn−−11>0 (n=1,2,…),上式等价于不等式组 )1(01,01<−<−nqq或>−>−01,01nqq②(n=1,2,…). 解①式,得q>1;解②式,由于n可为奇数、可为偶数,得-1<q<1.综上,q的取值范围是(-1,0)∪(0,+∞). (2)由bn=an+2-23an+1,得bn=an(q2-23q),∴Tn=(q2-23q)Sn. 于是Tn-Sn=Sn(q2-23q-1)=Sn(q+21)(q-2). 又∵Sn>0且-1<q<0或q>0, 当-1<q<-21或q>2时,Tn-Sn>0,即Tn>Sn; 当-21<q<2且q≠0时,Tn-Sn<0,即Tn<Sn; 当q=-21或q=2时,Tn-Sn=0,即Tn=Sn
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