(本小題滿分14分)
設(shè)數(shù)列
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的前
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項和為
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,且
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.
(1)求數(shù)列
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的通項公式;
(2)設(shè)
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,數(shù)列
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的前
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項和為
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,求證:
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.
(1)
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(2)略
(本小題滿分14分)
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解:當(dāng)
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時,

. ……1分
當(dāng)
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時,
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

. ……3分
∵

不適合上式,
∴

…4分
(2)證明: ∵
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.
當(dāng)
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時,
當(dāng)
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時,
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, ①
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. �、�
①-②得:
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得
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, ……8分
此式當(dāng)
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時也適合.
∴
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N
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.
∵
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,
∴
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. ……10分
當(dāng)
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時,
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,
∴
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. ……12分
∵

,
∴
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.
故
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,即
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.
綜上,
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. ……………..14分
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
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
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
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
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