已知數(shù)列
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滿足
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,且
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(n
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2且n∈N*).
(Ⅰ)求數(shù)列
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的通項公式;(5分)
(Ⅱ)設(shè)數(shù)列
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的前n項之和
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,求
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,并證明:
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.(7分)
(Ⅰ)
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.(Ⅱ)見解析
(Ⅰ)根據(jù)已知式子構(gòu)造關(guān)于
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的遞推式,從而利用數(shù)列的概念求出通項公式;(Ⅱ)利用錯位相減法求出數(shù)列的前n項和,再利用不等式的性質(zhì)證明不等式
(Ⅰ)
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且n∈N*),
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,…2分
即
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(
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,且
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N*),所以,數(shù)列
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是等差數(shù)列,公差
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,首項

,…3分
于是


.……5分
(Ⅱ)
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①
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②┈┈6分

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
………10分
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(12分)已知數(shù)列
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滿足
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
是

與

的等差中項
(1)證明:數(shù)列

是等比數(shù)列;
(2)求數(shù)列

的通項公式;
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(本小題滿分12分)等差數(shù)列
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中,
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,前

項和為

,等比數(shù)列

各項均為正數(shù),

,且
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,
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的公比
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(1)求
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與

;
(2)求
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已知
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是數(shù)列
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的前
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項和,且

(1)求數(shù)列

的通項公式;
(2)設(shè)各項均不為零的數(shù)列

中,所有滿足

的正整數(shù)

的個數(shù)稱為這個數(shù)列

的變號數(shù),令
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(n為正整數(shù)),求數(shù)列

的變號數(shù);
(3)記數(shù)列

的前

的和為

,若

對

恒成立,求正整數(shù)

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已知等差數(shù)列

(公差不為零)和等差數(shù)列

,如果關(guān)于

的方程

有解,那么以下九個方程已知等差數(shù)列

(公差不為零)和等差數(shù)列

,如果關(guān)于

的方程
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,

中,
無解的方程最多有
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A. | B. | C.2 | D.3 |
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中,
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( )
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為等差數(shù)列,公差為

,且

,則

( )
A.60 | B.85 | C. | D.其它值 |
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