本小題滿分12分)
已知數(shù)列

的前n項(xiàng)和為
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且


,

且

,數(shù)列
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滿足
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且


.
(I)求數(shù)列

的通項(xiàng)公式;
(II)求證:數(shù)列

為等比數(shù)列;
(III)求數(shù)列

前

項(xiàng)和的最小值.
解: (1)由

得

,

……2分
∴

………………4分
(2)當(dāng)

時(shí) ∵

,∴

,
∴
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;

又
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可證
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∴由上面兩式得

,
∴數(shù)列

是以-30為首項(xiàng),
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為公比的等比數(shù)列…………8分
(3)由(2)得

,∴


=

,∴
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是遞增數(shù)列 ………10分
當(dāng)
n=1時(shí),

<0;當(dāng)
n=2時(shí),

<0;當(dāng)
n=3時(shí),

<0;當(dāng)
n=4時(shí),

>0,所以,從

第4項(xiàng)起的各項(xiàng)均大于0,故前3項(xiàng)之和最小.
且

…………………………12分
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
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
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
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
}和{

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
=

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
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
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
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
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
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
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
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
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
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
,

前

項(xiàng)的積為

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
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
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
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
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
,

,

依次

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
滿足:

,


)
(1) 求數(shù)列

、

的通項(xiàng)公式;
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
的前n項(xiàng)的和

.
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對(duì)于數(shù)列

,定義.

,并對(duì)所有整數(shù)K >1定義

.若

,那么對(duì)所有

,使得

成立的k的最小值是_________
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已知數(shù)列{a
n}的前n項(xiàng)和為

,且

,則

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