已知在数列an中,a1=5/3且3an+1-an-2=0,求证丨an-1丨是等比数列,并求出an的通项公式设bn=log3 (an -1)^2/4,数列1/bnb(n+2)的前n项和为Tn,求证:Tn
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![已知在数列an中,a1=5/3且3an+1-an-2=0,求证丨an-1丨是等比数列,并求出an的通项公式设bn=log3 (an -1)^2/4,数列1/bnb(n+2)的前n项和为Tn,求证:Tn](/uploads/image/z/5091033-57-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%9C%A8%E6%95%B0%E5%88%97an%E4%B8%AD%2Ca1%3D5%2F3%E4%B8%943an%2B1-an-2%3D0%2C%E6%B1%82%E8%AF%81%E4%B8%A8an-1%E4%B8%A8%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%B9%B6%E6%B1%82%E5%87%BAan%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E8%AE%BEbn%3Dlog3+%28an+-1%29%5E2%2F4%2C%E6%95%B0%E5%88%971%2Fbnb%EF%BC%88n%2B2%EF%BC%89%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BATn%2C%E6%B1%82%E8%AF%81%EF%BC%9ATn)
已知在数列an中,a1=5/3且3an+1-an-2=0,求证丨an-1丨是等比数列,并求出an的通项公式设bn=log3 (an -1)^2/4,数列1/bnb(n+2)的前n项和为Tn,求证:Tn
已知在数列an中,a1=5/3且3an+1-an-2=0,求证丨an-1丨是等比数列,并求出an的通项公式
设bn=log3 (an -1)^2/4,数列1/bnb(n+2)的前n项和为Tn,求证:Tn
已知在数列an中,a1=5/3且3an+1-an-2=0,求证丨an-1丨是等比数列,并求出an的通项公式设bn=log3 (an -1)^2/4,数列1/bnb(n+2)的前n项和为Tn,求证:Tn
∵3a(n+1)-an-2=0→a(n+1)=1/3*an+2/3 ∴a(n+1)-1=1/3*(an-1) ∵a1-1=2/3 ∴{an-1}是以2/3为首项,1/3为公比的等比数列 ∴an-1=2/3*(1/3)^(n-1)=2/3^n ∴an=2/3^n+1
证明:3a(n+1)-an-2=0
则3a(n+1)=an+2
即3a(n+1)-3=an+2-3=an-1
所以:[a(n+1)-1]:an=1:3
故|a(n+1)-1]:(an-1)|=1/3