已知數(shù)列
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的前
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項和為
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滿足
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(
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)
(1)證明數(shù)列
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為等比數(shù)列;
(2)設(shè)
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,求數(shù)列
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的前
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項和
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試題分析:(1)根據(jù)已知
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求
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,當
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時,
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,然后兩式相減,利用
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,得到關(guān)于數(shù)列的遞推公式,
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;
(2)
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,由形式分析,
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的前n項和用錯位相減法求和,
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的前n項和用等差數(shù)列前n項和公式.
解:(1)
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兩式相減得:
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即:
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又因為
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所以數(shù)列
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為首項為
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公比為
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的等比數(shù)列
(2)由(1)知
所以
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令
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(1)
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(2)
(1)-(2)得
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故:
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求
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;2.等比數(shù)列的定義;3.錯位相減法.
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