已知點(1,

)是函數(shù)

且

)的圖象上一點,等比數(shù)列

的前

項和為

,數(shù)列
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
的首項為
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,且前
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項和

滿足

-

=

+
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(
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).
(1)求數(shù)列

和

的通項公式;
(2)求數(shù)列{

前

項和為

,問

>

的最小正整數(shù)

是多少?
(1)

,

;(2)112.
試題分析:(1)根據(jù)已知條件先求出

的表達式,這樣等比數(shù)列

前

項和

就清楚了,既然數(shù)列

是等比數(shù)列,我們可以用特殊值

來求出參數(shù)

的值,從而求出

,對數(shù)列

,由前

項和

滿足
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,可變形為
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,即數(shù)列
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為等差數(shù)列,可以先求出

,再求出

.(2)關(guān)鍵是求出和
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,而數(shù)列{
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前

項和
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就可用裂項相消法求出,再解不等式
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,得解.
試題解析:(1)
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,
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,
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
,

.
又數(shù)列

成等比數(shù)列,

,所以

; 2分
又公比
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,所以

; 4分

又

,

,

;
數(shù)列

構(gòu)成一個首相為1公差為1的等差數(shù)列,

,

當

,

;

(

); 8分
(2)




; 10分
由

得

,滿足

的最小正整數(shù)為112. 12分

項和

求數(shù)列通項;(2)裂項相消法求數(shù)列前

項和.
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
中,

;

是

與

的等比中項.
(I)求數(shù)列

的通項公式:
(II)若

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
的前

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
的前

項和為

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
,

.
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
和

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
的前

項和

.
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
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為等比數(shù)列,若

和

是方程
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+
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+

=
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的兩個根,則

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
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( )
A.12 | B.10 | C. | D. |
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科目:高中數(shù)學
來源:不詳
題型:單選題
在各項均為正數(shù)的等比數(shù)列
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中,
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,則
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( )
A.4 | B.6 | C.8 | D.8- |
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