數(shù)列

的各項(xiàng)均為正數(shù),
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為其前
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項(xiàng)和,對(duì)于任意
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,總有
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成等差數(shù)列.
(Ⅰ)求數(shù)列

的通項(xiàng)公式;
(Ⅱ)設(shè)數(shù)列
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的前
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項(xiàng)和為
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,且

,求證:對(duì)任意正整數(shù)

,總有
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
2;
(Ⅲ)正數(shù)數(shù)列
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中,
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,求數(shù)列

中的最大項(xiàng).
(Ⅰ)
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(Ⅱ)證明略
(Ⅲ)數(shù)列

中的最大項(xiàng)為
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(Ⅰ)解:由已知:對(duì)于
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,總有
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①成立
∴

(n ≥ 2)②
①--②得
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∴
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∵

均為正數(shù),∴

(n ≥ 2)
∴數(shù)列

是公差為1的等差數(shù)列
又n=1時(shí),

,解得

=1
∴

.(
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) …………4分(Ⅱ)證明:

,當(dāng)

時(shí),
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
…………8分
(Ⅲ)解:由已知
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,
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易得
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猜想
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時(shí),

是遞減數(shù)列.
令

∵當(dāng)

∴在

內(nèi)
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為單調(diào)遞減函數(shù)..
由

..
∴

時(shí),

是遞減數(shù)列.即

是遞減數(shù)列,
又

, ∴數(shù)列

中的最大項(xiàng)為
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. �!�12分
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題12分)已知數(shù)列

是等差數(shù)列,

;數(shù)列

的前n項(xiàng)和是

,且

.
(Ⅰ)求數(shù)列

的通項(xiàng)公式;
(II)求證:數(shù)列

是等比數(shù)列;
(Ⅲ)記

,求

的前n項(xiàng)和

.
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已知數(shù)列

是首項(xiàng)

公比

的等比數(shù)列,設(shè)數(shù)列

的通
項(xiàng)

,數(shù)列

、

的前

項(xiàng)和分別為

.如果

對(duì)
一切自然數(shù)

都成立,求實(shí)數(shù)

的取值范圍.
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(12分)設(shè)數(shù)列

的前

項(xiàng)和為

,數(shù)列

為等比數(shù)列,且

,

。(1)求數(shù)列

和

的通項(xiàng)公式; (2)設(shè)

,求數(shù)列

的前

項(xiàng)和

。
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來源:不詳
題型:解答題
(本小題滿分12分)
設(shè)各項(xiàng)均為正數(shù)的數(shù)列

的前n項(xiàng)和為

,已知

,數(shù)列

是公差為

的等差數(shù)列。
(1)求數(shù)列

的通項(xiàng)公式(用

表示);
(2)設(shè)

為實(shí)數(shù),對(duì)滿足

的任意正整數(shù)

,不等式

都成立。求證:

的最大值為

。
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(14分)等差數(shù)列

中,前三項(xiàng)分別為

,前

項(xiàng)和為

(1)、求
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和
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; (2)、求T=
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。
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知等差數(shù)列1,
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,等比數(shù)列3,
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,則該等差數(shù)列的公差為( )
A.3或 | B.3或-2 | C.3 | D.-2 |
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