設(shè)數(shù)列
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的前項n和為
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,若對于任意的正整數(shù)n都有
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.
(1)求
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的通項公式。
(2)求數(shù)列
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的前n項和.
(1)
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對于任意的正整數(shù)都成立,
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兩式相減,得
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∴
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, 即
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,即
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對一切正整數(shù)都成立。
∴數(shù)列
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是等比數(shù)列。由已知得
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即
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∴數(shù)列
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的首項
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,公比
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,
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。
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。
(2)
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本題滿分12分) 已知點(1,
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)是函數(shù)
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且
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)的圖象上一點,等比數(shù)列
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的前
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項和為
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,數(shù)列
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
的首項為
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,且前
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項和
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滿足
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-
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=
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+
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(
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).
(1)求數(shù)列
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和
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的通項公式;
(2)若數(shù)列{
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前
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項和為
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,問
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>
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的最小正整數(shù)
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是多少?
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
將數(shù)列{a
n}中的所有項按每一行比上一行多一項的規(guī)則排成如下數(shù)表:
a
1a
2 a
3a
4 a
5 a
6a
7 a
8 a
9 a
10……記表中的第一列數(shù)a
1,a
2,a
4,a
7,…構(gòu)成的數(shù)列為{b
n},b
1=a
1="1." S
n為數(shù)列{b
n}的前n項和,且滿足
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=1(n≥2).
(Ⅰ)證明數(shù)列{
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}成等差數(shù)列,并求數(shù)列{b
n}的通項公式;
(Ⅱ)上表中,若從第三行起,每一行中的數(shù)按從左到右的順序均構(gòu)成等比數(shù)列,且公比為同一個正數(shù).當
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時,求上表中第k(k≥3)行所有項的和.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分13分)
設(shè)數(shù)列
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的前
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項和為
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,點
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在直線
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上,(
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為常數(shù),
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,
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).
(1)求
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;
(2)若數(shù)列
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的公比
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,數(shù)列
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滿足
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,
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,
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,求證:
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為等差數(shù)列,并求
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;
(3)設(shè)數(shù)列
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滿足
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,
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為數(shù)列
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的前
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項和,且存在實數(shù)
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滿足
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
,求
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的最大值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
兩個等差數(shù)列
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和
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,其前
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項和分別為
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,且
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則
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等于( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知一個等差數(shù)列的前四項之和為21,末四項之和為67,前
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項和為286,則項數(shù)
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為( )
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