.已知等比數(shù)列
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的各項(xiàng)均為正數(shù),且
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.
(Ⅰ)求數(shù)列
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的通項(xiàng)公式;
(Ⅱ)設(shè)
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,求數(shù)列
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的前n項(xiàng)和.
(Ⅲ)設(shè)
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,求數(shù)列{
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}的前
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項(xiàng)和.
解:(Ⅰ)設(shè)數(shù)列{a
n}的公比為q,由
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得
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,所以
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.
由條件可知
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,故
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.由
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得
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,所以
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.
故數(shù)列{a
n}的通項(xiàng)公式為a
n=
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.
(Ⅱ)
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
,
故
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,
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,
所以數(shù)列
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的前n項(xiàng)和為
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.
(Ⅲ)由
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=
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.由錯(cuò)位相減法得其前
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和為
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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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
項(xiàng)和為
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=
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