在數(shù)列
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中,
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
.
(Ⅰ)求證:數(shù)列
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為等差數(shù)列;
(Ⅱ)設(shè)數(shù)列

滿足
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,若
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
對一切
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且
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恒成立,求實數(shù)

的取值范圍
解:(1)由
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,變形得:
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即
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,所以
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………………4分
故數(shù)列
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是以
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為首項,
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為公差的等差數(shù)列………………………5分
(2)由(1)得
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,所以
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…………………………7分
設(shè)
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=
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=
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=
所以
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是關(guān)于
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的單調(diào)遞增函數(shù),則
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故實數(shù)

的取值范圍是
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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14分)
已知數(shù)列

為等差數(shù)列,且

,

.
(1) 求數(shù)列

的通項公式;
(2) 令

,求證:數(shù)列

是等比數(shù)列;
(3)令

,求數(shù)列

的前

項和

.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知等差數(shù)列{

}的前n項和為

,若

,則

=( )
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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14分)設(shè){a
n}是等差數(shù)列,{b
n}是各項都為正數(shù)的等比數(shù)列,且
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1=1,a
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5=21,a
5+b
3=13.
(Ⅰ)求{a
n},{b
n
}的通項公式;
(Ⅱ)求數(shù)列

的前n項和

.
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來源:不詳
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已知等差數(shù)列{
an}的前
n項的和記為
Sn.如果
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a8=-4.
(1)求數(shù)列{
an}的通項公式;
(2)求
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n的值;
(3)從數(shù)列{
an}中依次取出
a1,
a2,
a4,
a8,…,

,…,構(gòu)成一個新的數(shù)列{
bn},求{
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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14分)已知

,點

在曲線

上

且

(Ⅰ)求證:數(shù)列

為等差數(shù)列,并求數(shù)列

的通項公式;
(Ⅱ)設(shè)數(shù)列

的前
n項和為

,若對于任意的

,存在正整數(shù)
t,使得

恒成立,求最小正整數(shù)
t的值
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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

的前

項和為

,數(shù)列

滿足:

,前

項和為

,設(shè)

。 (1)求數(shù)列

的通項公式;
(2)是否存在自然數(shù)k, 當(dāng)

時,總有

成立,若存在,求自然數(shù)

的最小值。若不存在,說明理由。
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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

,

,

,

(1)令

,證明:

是等比數(shù)列;
(2)求

的通項公式
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
(本題滿分14分)已知

,點

在曲線

上

且

(Ⅰ)求證:數(shù)列

為等差數(shù)列,并求數(shù)列

的通項公式;
(Ⅱ)設(shè)數(shù)列

的前n項和為

,若對于任意的

,存在正整數(shù)t,使得

恒成立,求最小正整數(shù)t的值.
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