已知數(shù)列
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的前

項和為
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,
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,且
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(
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為正整數(shù))
(Ⅰ)求出數(shù)列

的通項公式;
(Ⅱ)若對任意正整數(shù)
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,
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恒成立,求實數(shù)

的最大值
(1)
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(
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為正整數(shù)).
(2)實數(shù)
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的最大值為1.
(I)再構(gòu)造一個當
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時,
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然后與
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作差,可得到
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,從而可知是

等比數(shù)列,問題得解.
(II)此題的關(guān)鍵是求S
n的最小值,要先根據(jù)前n項和公式求出S
n,然后從函數(shù)的角度研究其單調(diào)性確定其最值即可.
(1)
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
, ①
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當

時,
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. ②
由 ① - ②,得
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.


.
又
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,
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,解得
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.

數(shù)列
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是首項為1,公比為

的等比數(shù)列.

(

為正整數(shù)). ……………………6分
(2)由(Ⅰ)知
由題意可知,對于任意的正整數(shù)

,恒有

,

數(shù)列
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單調(diào)遞增, 當
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時,該數(shù)列中的最小項為
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,

必有
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,即實數(shù)

的最大值為1.
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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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
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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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