已知數(shù)列
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滿(mǎn)足

。定義數(shù)列
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,使得
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,
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。若4<
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< 6,則數(shù)列
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的最大項(xiàng)為
由

知:
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,所以數(shù)列

是公差為-2的等差數(shù)列,所以

.

。

當(dāng)時(shí)
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時(shí),

;當(dāng)

時(shí),

所以數(shù)列

的最大項(xiàng)為
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
已知數(shù)列

,定義其平均數(shù)是

,

.
(Ⅰ)若數(shù)列

的平均數(shù)

,求

;
(Ⅱ)若數(shù)列

是首項(xiàng)為1,公比為2的等比數(shù)列,其平均數(shù)為

,
求證:

.
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(本小題滿(mǎn)分13分)已知數(shù)列

.如果數(shù)列

滿(mǎn)足

,

,其中

,則稱(chēng)

為

的“衍生數(shù)列”.
(Ⅰ)若數(shù)列

的“衍生數(shù)列”是

,求
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;
(Ⅱ)若

為偶數(shù),且

的“衍生數(shù)列”是

,證明:

的“衍生數(shù)列”是

;
(Ⅲ)若

為奇數(shù),且

的“衍生數(shù)列”是

,

的“衍生數(shù)列”是

,….依次將數(shù)列

,

,

,…的第

項(xiàng)取出,構(gòu)成數(shù)列

.證明:

是等差數(shù)列.
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(本小題滿(mǎn)分18分) 本題共有3個(gè)小題,第1小題滿(mǎn)分4分,第2小題滿(mǎn)分6分,第3小題滿(mǎn)分8分.
(文)已知數(shù)列

中,

(1)求證數(shù)列

不是等比數(shù)列,并求該數(shù)列的通項(xiàng)公式;
(2)求數(shù)列

的前

項(xiàng)和

;
(3)設(shè)數(shù)列

的前

項(xiàng)和為

,若

對(duì)任意

恒成立,求

的最小值.
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
已知數(shù)列

的前

項(xiàng)和為

,且

是

與2的等差中項(xiàng),數(shù)列

滿(mǎn)足

,點(diǎn)

在直線(xiàn)

上,
(1)求數(shù)列

,

的通項(xiàng)公式;
(2)設(shè)

,求數(shù)列

的前

項(xiàng)和

.
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(本小題滿(mǎn)分12分)
已知數(shù)列

的前

項(xiàng)和

.
(Ⅰ)求數(shù)列{

}的通項(xiàng)公式;
(Ⅱ)設(shè)

,求數(shù)列{

}的前

項(xiàng)和.
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(本小題滿(mǎn)分12分)已知數(shù)列{
an}的前
n項(xiàng)和為
Sn,且
an是
Sn與2的等差中項(xiàng),數(shù)列{
bn}中,
b1=1,點(diǎn)P(
bn,
bn+1)在直線(xiàn)

上。
(1)求
a1和
a2的值;
(2)求數(shù)列{
an},{
bn}的通項(xiàng)
an和
bn;
(3)設(shè)
cn=
an·
bn,求數(shù)列{
cn}的前n項(xiàng)和
Tn.
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
(本小題滿(mǎn)分12分)設(shè)
Sn是正項(xiàng)數(shù)列

的前
n項(xiàng)和,

.(I)求數(shù)列

的通項(xiàng)公式;(II)

的值.
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:解答題
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