(本小題滿分12分)
等比數(shù)列{
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}的前
n項和為
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,已知對任意的
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,點
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,均在函數(shù)
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且
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均為常數(shù))的圖像上。
(1)求
r的值;
(11)當
b=2時,記
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,證明:對任意的
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,不等式
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成立。
(1)
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(11)證明見解析。
因為對任意的
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,點
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,均在函數(shù)

且
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均為常數(shù)的圖像上.所以得
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,當
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時,
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,當

時,
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,又因為{

}為等比數(shù)列,所以
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,公比為
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,
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(2)當b=2時,

,

則

,所以

下面用數(shù)學歸納法證明不等式

成立。
①當

時,左邊=
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,右邊=

,因為

,所以不等式成立.
②假設當

時不等式成立,即
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成立.則當

時,左邊=


所以當

時,不等式也成立.
由①、②可得不等式恒成立。
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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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
的前

項和為

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
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(Ⅱ)若

,數(shù)列

}滿足

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