已知等差數(shù)列
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滿足,
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,則前n項和
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取最大值時,n的值為( )
試題分析:因為等差數(shù)列的前n項和公式
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,可以看做關(guān)于n的二次函數(shù),因此我們可以利用二次函數(shù)求最值解決本題.由已知
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代入求和公式得
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.對稱軸為
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所以答案為B
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科目:高中數(shù)學
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已知數(shù)列

的前
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項和
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,求證:
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是等比數(shù)列,并求出通項公式.
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科目:高中數(shù)學
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已知數(shù)列

的前
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項的和為
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,
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,求證:數(shù)列
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為等差數(shù)列的充要條件是
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.
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設等比數(shù)列
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的首項為
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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;數(shù)列
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滿足
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(
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).
(1)求數(shù)列
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的通項公式;
(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
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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
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是數(shù)列
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的前
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項和,試求滿足
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的所有正整數(shù)
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.
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來源:不詳
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數(shù)列
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的前
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項和為
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,若
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,點
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在直線
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上.
⑴求證:數(shù)列
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是等差數(shù)列;
⑵若數(shù)列
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滿足
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,求數(shù)列
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的前
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項和
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;
⑶設
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,求證:
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.
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對于數(shù)列
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,規(guī)定
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為數(shù)列
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的一階差分數(shù)列,其中
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.對自然數(shù)
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,規(guī)定
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為數(shù)列
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的
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階差分數(shù)列,其中
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⑴若
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,則
;
⑵若
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,且滿足
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,則數(shù)列
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的通項公式為
.
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已知函數(shù)
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對任意的實數(shù)
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都有
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,且
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,則
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已知等差數(shù)列
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前
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項和為
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,且
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+
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=13,
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=35,則
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=( )
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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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項的和
.
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