將數(shù)列
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中的所有項(xiàng)按每一行比上一行多一項(xiàng)的規(guī)則排成下表:
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
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……
記表中的第一列數(shù)
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、
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、
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、
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……構(gòu)成的數(shù)列為
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,
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,
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為數(shù)列
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的前
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項(xiàng)和,且滿(mǎn)足
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(I)證明數(shù)列

成等差數(shù)列,并求數(shù)列

的通項(xiàng)公式;
(II)上表中,若從第三行起,每一行中的數(shù)從左到右的順序均構(gòu)成等比數(shù)列,且公比為同一個(gè)正數(shù),當(dāng)

時(shí),求上表中第
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行所有項(xiàng)的和
(I)
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(II)
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(I)證明:當(dāng)
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時(shí),
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


又
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,所以數(shù)列
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是首項(xiàng)為1,公差為
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的等差數(shù)列。
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所以
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時(shí)

因此
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(II)設(shè)上表中從第三行起,每行的公比都為

,且
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表中到12行尾共含數(shù)列

的前78項(xiàng),
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是表中第13行第三列,
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,
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記表中第
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行所有項(xiàng)的和為

,則
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科目:高中數(shù)學(xué)
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題型:解答題
數(shù)列

為等差數(shù)列,

為正整數(shù),其前

項(xiàng)和為

,數(shù)列

為等比數(shù)列,且

,數(shù)列

是公比為64的等比數(shù)列,

.
(1)求

;
(2)求證

.
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科目:高中數(shù)學(xué)
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已知數(shù)列

,

,

,

,

,…,這個(gè)數(shù)列的特點(diǎn)是從第二項(xiàng)起,每一項(xiàng)都等于它的前后兩項(xiàng)之和,則這個(gè)數(shù)列的前

項(xiàng)之和

=
.
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
中,已知角A、B、C成等差數(shù)列,且

成等比數(shù)列,則

是( )
A.鈍角三角形 B.直角三角形 C.含

的不等邊三角形 D.等比三角形
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科目:高中數(shù)學(xué)
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已知數(shù)列

中,

,對(duì)于任意的

,有

(1)求數(shù)列

的通項(xiàng)公式;
(2)若數(shù)列

滿(mǎn)足:

求數(shù)列

的通項(xiàng)公式;
(3)設(shè)

,是否存在實(shí)數(shù)

,當(dāng)

時(shí),

恒成立,若存在,求實(shí)數(shù)

的取值范圍,若不存在,請(qǐng)說(shuō)明理由.
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已知在公比為實(shí)數(shù)的等比數(shù)列

中,

,且

,

,

成等差數(shù)列.
(Ⅰ)求數(shù)列

的通項(xiàng)公式;
(Ⅱ)設(shè)數(shù)列

的前
n項(xiàng)和為

,求

的最大值.
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科目:高中數(shù)學(xué)
來(lái)源:不詳
題型:填空題
等差數(shù)列{
an}中有兩項(xiàng)
am和
ak滿(mǎn)足
am=

,
ak=

,則該數(shù)列前
mk項(xiàng)之和是
.
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數(shù)列

滿(mǎn)足

="1,"

=

,且

(
n≥2),

則

等于( )
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