(本小題滿分12分)已知等差數(shù)列
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的公差大于0,且
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是方程
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的兩根,數(shù)列
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的前n項(xiàng)的和為
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,且
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.
(1) 求數(shù)列
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,
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的通項(xiàng)公式;
(2)記
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,求證:
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.
(Ⅰ)∵a
3,a
5是方程
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的兩根,且數(shù)列
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的公差d>0,
∴a
3=5,a
5=9,公差
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∴
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………………3分
又當(dāng)n=1時(shí),有b
1=S
1=1-
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當(dāng)
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∴數(shù)列{b
n}是等比數(shù)列,
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∴
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…………6分
(Ⅱ)由(Ⅰ)知
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…………9分
∴
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∴
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…………………………12分
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(理)數(shù)列
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的前
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項(xiàng)和記為
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(Ⅰ)求
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的通項(xiàng)公式;
(Ⅱ)等差數(shù)列
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的各項(xiàng)為正,其前
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項(xiàng)和為
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,且
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,又
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成等比數(shù)列,求
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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
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分)設(shè)數(shù)列
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的前
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項(xiàng)和為
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,且
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,
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.
(Ⅰ)求
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,
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,
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,并求出數(shù)列
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的通項(xiàng)公式;
(Ⅱ)設(shè)數(shù)列
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的前
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項(xiàng)和為
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,試求
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的取值范圍.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題12分)
已知數(shù)列
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滿足
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,
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,等比數(shù)列
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的首項(xiàng)為2,公比為
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。
(Ⅰ)若
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,問
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等于數(shù)列
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中的第幾項(xiàng)?
(Ⅱ)數(shù)列
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和
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的前
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項(xiàng)和分別記為
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和
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,
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的最大值為
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,當(dāng)
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時(shí),試比較
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與
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的大小
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來源:不詳
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設(shè)各項(xiàng)為正的數(shù)列
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的前
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項(xiàng)和為
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且滿足:
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(Ⅰ)求
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;(Ⅱ)若
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求證:
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來源:不詳
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(本小題10分)
已知等差數(shù)列
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,
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,

,且項(xiàng)

分別是某一等比數(shù)列
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中的第
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項(xiàng),(1)求數(shù)列
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的第12項(xiàng); (2)求數(shù)列
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的第
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項(xiàng)。
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
若數(shù)列{


} (n∈N

)是等差數(shù)列,則通項(xiàng)為b

=
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(n∈N

)的數(shù)列也是等差數(shù)列;類比上述性質(zhì),相應(yīng)地:若數(shù)列{

}是等比數(shù)列,且

>0(n∈N

),則通項(xiàng)為
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=
*** (n∈N
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)的數(shù)列也是等比數(shù)列。
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科目:高中數(shù)學(xué)
來源:不詳
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在等比數(shù)列

中,

,前4項(xiàng)和為1111,則該數(shù)列的公比為( )

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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(14分)已知數(shù)列
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滿足
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,

(1)求
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。(2)由(1)猜想

的通項(xiàng)公式。
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(3)用數(shù)學(xué)歸納法證明(2)的結(jié)果。
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