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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(12分)(2011•湖北)成等差數(shù)列的三個正數(shù)的和等于15,并且這三個數(shù)分別加上2、5、13后成為等比數(shù)列{b
n}中的b
3、b
4、b
5.
(Ⅰ)求數(shù)列{b
n}的通項公式;
(Ⅱ)數(shù)列{b
n}的前n項和為S
n,求證:數(shù)列{S
n+
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}是等比數(shù)列.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知正項數(shù)列
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中,其前
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項和為
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,且
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.
(1)求數(shù)列

的通項公式;
(2)設(shè)

是數(shù)列

的前

項和,

是數(shù)列

的前

項和,求證:
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列
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和
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滿足:
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,其中
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為實數(shù),

為正整數(shù).
(1)對任意實數(shù)

,求證:

不成等比數(shù)列;
(2)試判斷數(shù)列

是否為等比數(shù)列,并證明你的結(jié)論.
(3)設(shè)

為數(shù)列

的前
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項和.是否存在實數(shù)

,使得對任意正整數(shù)

,都有
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?若存在,求

的取值范圍;若不存在,說明理由.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列

的各項均為正數(shù),記
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,
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,

.
(1)若
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,且對任意

,三個數(shù)
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組成等差數(shù)列,求數(shù)列

的通項公式.
(2)證明:數(shù)列
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是公比為

的等比數(shù)列的充分必要條件是:對任意

,三個數(shù)

組成公比為

的等比數(shù)列.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知等差數(shù)列前三項為

,前

項的和為

.
(1)求

;
(2)求

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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
首項為
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的等差數(shù)列,從第
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項起開始為正數(shù),則公差

的取值范圍是( ).
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
數(shù)列
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…中的
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等于( )
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