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设数列{an}的首项a1=1,其前n项和Sn满足:3tSn-(2t+3)Sn-1=3t(t...
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设数列{a
n}的首项a
1=1,其前n项和S
n满足:3tS
n-(2t+3)S
n-1=3t(t>0,n=2,3,…).
(Ⅰ)求证:数列{a
n}为等比数列;
(Ⅱ)记{a
n}的公比为f(t),作数列{b
n},使b
1=1,
,求和:b
1b
2-b
2b
3+b
3b
4-b
4b
5+…+b
2n-1b
2n-b
2nb
2n+1.
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