已知數(shù)列
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中,
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.
(1)設(shè)
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,求證:數(shù)列
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是常數(shù)列,并寫出其通項公式;
(2)設(shè)

,求證:數(shù)列

是等比數(shù)列,并寫出其通項公式;
(3)求數(shù)列

的通項公式.
(1)利用常數(shù)列的定義即證:b
n+1=b
n即可.
(2)利用等比數(shù)列的定義證明:

再進(jìn)一步證明出其比值是一個與n無關(guān)的常數(shù)即可.
(3)在(2)的基礎(chǔ)上,可由

,通過疊加的方法求a
n即可
(1)證明:∵
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∴
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又∵
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∴
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∴
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是常數(shù)列,且
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……………(3分)

……(4分)
(2)證明∵

∴
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又∵
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∴
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而

∴
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是以2為首項,2為公比的等比數(shù)列………………(7分)
∴
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…………(8分)
(3)解:
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①
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②
②-①得
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科目:高中數(shù)學(xué)
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(本題滿分14分)已知等差數(shù)列

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的前

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
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
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
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
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
時,
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取得最小值.
(Ⅰ)求數(shù)列

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
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
,如果

是單調(diào)數(shù)列,求實數(shù)

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
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
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
.
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
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
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
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
的前
n項和

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
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
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已知

是等差數(shù)列

的前

項和,且

.
(1)求

;
(2)令

,計算

和

,由此推測數(shù)列

是等差數(shù)列還是等比數(shù)列,證明你的結(jié)論.
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
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已知數(shù)列

中,

,

,

是數(shù)列

的前

項和,且

,

.
(1)求

的值;
(2)求數(shù)列

的通項公式;
(3)若

是數(shù)列

的前

項和,且

對一切

都成立,求實數(shù)

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A. | B. | C.2 | D.3 |
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