已知数列{An}是首项为a且公比q不等于1得等比数列,Sn是其前n项和,A1,2A7,3A4成等差数列.(1)证明,12S3,S6,S12-S6成等差数列(2)求和:Tn=A1+2A4+3A7+.+nA3n-2
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![已知数列{An}是首项为a且公比q不等于1得等比数列,Sn是其前n项和,A1,2A7,3A4成等差数列.(1)证明,12S3,S6,S12-S6成等差数列(2)求和:Tn=A1+2A4+3A7+.+nA3n-2](/uploads/image/z/5602562-26-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7BAn%7D%E6%98%AF%E9%A6%96%E9%A1%B9%E4%B8%BAa%E4%B8%94%E5%85%AC%E6%AF%94q%E4%B8%8D%E7%AD%89%E4%BA%8E1%E5%BE%97%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2CSn%E6%98%AF%E5%85%B6%E5%89%8Dn%E9%A1%B9%E5%92%8C%2CA1%2C2A7%2C3A4%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97.%EF%BC%881%EF%BC%89%E8%AF%81%E6%98%8E%2C12S3%2CS6%2CS12-S6%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%EF%BC%882%EF%BC%89%E6%B1%82%E5%92%8C%EF%BC%9ATn%3DA1%2B2A4%2B3A7%2B.%2BnA3n-2)
已知数列{An}是首项为a且公比q不等于1得等比数列,Sn是其前n项和,A1,2A7,3A4成等差数列.(1)证明,12S3,S6,S12-S6成等差数列(2)求和:Tn=A1+2A4+3A7+.+nA3n-2
已知数列{An}是首项为a且公比q不等于1得等比数列,Sn是其前n项和,A1,2A7,3A4成等差数列.
(1)证明,12S3,S6,S12-S6成等差数列
(2)求和:Tn=A1+2A4+3A7+.+nA3n-2
已知数列{An}是首项为a且公比q不等于1得等比数列,Sn是其前n项和,A1,2A7,3A4成等差数列.(1)证明,12S3,S6,S12-S6成等差数列(2)求和:Tn=A1+2A4+3A7+.+nA3n-2
An=A1*q^(n-1),2*2A7=A1+3A4得4A1*q^6=A1+3A1*q^3,所以
4q^6=1+3q^3,设q^3=t,则4t^2-3t-1=0,得t=-1/4或1(舍弃),
即q^3=-1/4,之后.不想写了,不好意思
是证成等比数列吧
利用上楼答案1-q^6=15/16 1-q^3=5/4 1-q^12=255/256
2S6-(12S3+S12-S6)=3S6-12S3-S12=a[3(1-q^6)-12(1-q^3)-(1-q^12)]/(1-q)
题目不对啊 ,怎么正不出来
4a7=a1+3a4
4a1*q^6=a1+3a1*q^3
4q^6=1+3q^3
令q^3=t
4t^2-3t-1=0
t1=1 t2=-1/4
q不等于1
q^3=-1/4
q=(-1/4)^(1/3)
q=-2^(2/3)
证明2S6=12S3+S12-S6
证明3S6=12S3+S12
左=3a...
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4a7=a1+3a4
4a1*q^6=a1+3a1*q^3
4q^6=1+3q^3
令q^3=t
4t^2-3t-1=0
t1=1 t2=-1/4
q不等于1
q^3=-1/4
q=(-1/4)^(1/3)
q=-2^(2/3)
证明2S6=12S3+S12-S6
证明3S6=12S3+S12
左=3a1(1-t^2)/(1-q)=3(1-t^2)[a1/(1-q)]
右=[12a1(1-t)+a1(1-t^4)]/(1-q)=(13-12t-t^4)[a1/(1-q)]=(1-t^2)(t^2+13)[a1/(1-q)]
t^2+13不等于3
题出的可真有水平,怎么把不等式证成等式呢?期待高手出现……
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