已知等差數(shù)列
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滿足
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,
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,則此數(shù)列的前
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項(xiàng)的和
.
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.
試題分析:法一:由于數(shù)列
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是等差數(shù)列,
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,
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;法二:設(shè)等差數(shù)列
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的公差為
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,則
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,解得
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,
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)等比數(shù)列
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的首項(xiàng)為
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,公比為
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(
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為正整數(shù)),且滿足
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是
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與
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的等差中項(xiàng);數(shù)列
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滿足
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(
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).
(1)求數(shù)列

的通項(xiàng)公式;
(2)試確定
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的值,使得數(shù)列
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為等差數(shù)列;
(3)當(dāng)
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為等差數(shù)列時,對每個正整數(shù)
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,在
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與
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之間插入
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個2,得到一個新數(shù)列
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. 設(shè)
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是數(shù)列
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的前
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項(xiàng)和,試求滿足
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的所有正整數(shù)
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知
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為等差數(shù)列
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的前
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項(xiàng)和,且
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.
(Ⅰ)求
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的通項(xiàng)公式;
(Ⅱ)求數(shù)列

的前
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項(xiàng)和
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)數(shù)列

的前
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項(xiàng)和

滿足
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,其中
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.
⑴若
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,求
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及
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;
⑵若
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,求證:
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,并給出等號成立的充要條件.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
數(shù)列

的前

項(xiàng)和為
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,若
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,點(diǎn)
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在直線
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上.
⑴求證:數(shù)列

是等差數(shù)列;
⑵若數(shù)列

滿足

,求數(shù)列
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的前
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項(xiàng)和
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;
⑶設(shè)
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,求證:
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知函數(shù)
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對任意的實(shí)數(shù)
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都有
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,且
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,則
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
已知

,各項(xiàng)均為正數(shù)的數(shù)列
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滿足
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,若
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,則
.
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科目:高中數(shù)學(xué)
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題型:填空題
數(shù)列
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滿足
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

分別表示
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的整數(shù)部分與分?jǐn)?shù)部分),則
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.
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