設(shè)數(shù)列
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是等比數(shù)列,
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,公比
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是
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的展開式中的第二項(xiàng)(按x的降冪排列).
(1)用
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表示通項(xiàng)
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與前n項(xiàng)和
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;
(2)若
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,用
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表示
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.
試題分析:解:(1)∵
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∴
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∴
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, 2分
由
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的展開式中的同項(xiàng)公式知
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,
∴
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∴
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4分
(2)當(dāng)
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時,
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,
又∵
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,
∴
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, ∴
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,
當(dāng)x≠1時,
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,
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∴
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10分
點(diǎn)評:主要是考查了數(shù)列的求和以及組合數(shù)性質(zhì)的運(yùn)用,屬于中檔題。
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
對于給定數(shù)列
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,如果存在實(shí)常數(shù)
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使得
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對于任意

都成立,我們稱數(shù)列

是“
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數(shù)列”.
(Ⅰ)若
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,
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,
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,數(shù)列
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、
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是否為“

數(shù)列”?若是,指出它對應(yīng)的實(shí)常數(shù)
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,若不是,請說明理由;
(Ⅱ)證明:若數(shù)列
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是“
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數(shù)列”,則數(shù)列
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也是“
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數(shù)列”;
(Ⅲ)若數(shù)列
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滿足

,
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,
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為常數(shù).求數(shù)列

前
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項(xiàng)的和.
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題型:解答題
已知等差數(shù)列

中,

①求數(shù)列

的通項(xiàng)公式;
②若數(shù)列

前
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項(xiàng)和
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,求
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的值。
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若等差數(shù)列
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滿足:

,且公差

,其前

項(xiàng)和為
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.則滿足

的

的最大值為( )
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已知數(shù)列{a
n}的前n項(xiàng)和
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,且S
n的最大值為8,則a
2=
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如圖,將正

分割成16個全等的小正三角形,在每個三角形的頂點(diǎn)各放置一個數(shù),使位于同一直線上的點(diǎn)放置的數(shù)(當(dāng)數(shù)的個數(shù)不少于3時)都分別依次成等差數(shù)列,若頂點(diǎn)

處的三個數(shù)互不相同且和為1,則所有頂點(diǎn)的數(shù)之和
.

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已知等差數(shù)列{
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}中,

=14,前10項(xiàng)和
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. (1)求
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;
(2)將{

}中的第2項(xiàng),第4項(xiàng),…,第

項(xiàng)按原來的順序排成一個新數(shù)列{

},令

,求數(shù)列{

}的前

項(xiàng)和

.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列

滿足
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(1)設(shè)
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是公差為

的等差數(shù)列.當(dāng)

時,求
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的值;
(2)設(shè)
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求正整數(shù)

使得一切
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均有
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
數(shù)列

的通項(xiàng)公式是

,若前n項(xiàng)的和為11,則n=______
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