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设等比数列{an}的前n项和Sn,首项a1=1,公比.(Ⅰ)证明:Sn=(1+λ)-λan...
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设等比数列{a
n}的前n项和S
n,首项a
1=1,公比
.
(Ⅰ)证明:S
n=(1+λ)-λa
n;
(Ⅱ)若数列{b
n}满足
,b
n=f(b
n-1)(n∈N
*,n≥2),求数列{b
n}的通项公式;
(Ⅲ)若λ=1,记
,数列{c
n}的前项和为T
n,求证:当n≥2时,2≤T
n<4.
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设等比数列{an}的前n项和Sn,首项a1=1,公比.
(Ⅰ)证明:Sn=(1+λ)-λan;
(Ⅱ)若数列{bn}满足,bn=f(bn-1)(n∈N*,n≥2),求数列{bn}的通项公式;
(Ⅲ)若λ=1,记,数列{cn}的前项和为Tn,求证:当n≥2时,2≤Tn<4.
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(Ⅱ)若数列{bn}满足,bn=f(bn-1)(n∈N*,n≥2),求数列{bn}的通项公式;
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