已知數(shù)列
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的前
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項和為
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,
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.
(1)求證:數(shù)列
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是等比數(shù)列;
(2)若
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,求實數(shù)
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的取值范圍.
(1)詳見解析; (2)
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;
試題分析:(1)由前n項的和
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與
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an的關系
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,得到數(shù)列的遞推公式,注意分析a是否為零,再求數(shù)列的通項公式.
(2)利用極限的值和第(1)的結(jié)果,代入
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整理出關于n的式子,再求n的值.
試題解析:(1)當
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時,
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,
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,
∵
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, ∴
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; 1分
當
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時,
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,

, 4分
∵
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, ∴ 數(shù)列
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是等比數(shù)列; 5分
(2)∵
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, ∴ 公比
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, 7分
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,
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, 9分
∴實數(shù)
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的取值范圍是
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. 10分.
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科目:高中數(shù)學
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題型:解答題
已知數(shù)列

的前

項和為

,數(shù)列

滿足:


。
(1)求數(shù)列

的通項公式

;
(2)求數(shù)列

的通項公式

;(3)若

,求數(shù)列

的前

項和
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.
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已知數(shù)列

的前

項和

滿足

,又

,

.
(1)求實數(shù)k的值;
(2)問數(shù)列
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是等比數(shù)列嗎?若是,給出證明;若不是,說明理由;
(3)求出數(shù)列

的前
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項和
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.
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已知等比數(shù)列

中,
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,

.
(1)求數(shù)列

的通項公式;
(2)若
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,

分別為等差數(shù)列

的第3項和第5項,試求數(shù)列

的通項公式及前

項和

.
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在數(shù)列

中,前n項和為

,且
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.
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
的通項公式;
(Ⅱ)設

,數(shù)列

前n項和為

,求
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的取值范圍.
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設等差數(shù)列

的公差

,

,若

是

與

的等比中項,則
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=( )
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在等差數(shù)列

中,

,

,則該數(shù)列前20項的和為____.
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已知數(shù)列

為等差數(shù)列,若

,

,則
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( )
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