(本小題滿分14分)已知等差數(shù)列
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的前
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項(xiàng)和為
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,前
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項(xiàng)和為
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.
1)求數(shù)列
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的通項(xiàng)公式
2)設(shè)
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, 求數(shù)列
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的前
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項(xiàng)和
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.
(1)
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;(2)S
n=
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。
試題分析:(1)設(shè){a
n}的公差為d ,由已知得
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解得a
1=3,d=-1
故a
n=3-(n-1)(-1)=4-n…………………………………………6分
(2)由(1)的解答得,b
n=n·q
n-1,于是
S
n=1·q
0+2·q
1+3·q
2+……+(n-1)·q
n-1+n·q
n.
若q≠1,將上式兩邊同乘以q,得
qS
n=1·q
1+2·q
2+3·q
3+……+(n-1)·q
n+n·q
n+1.
將上面兩式相減得到
(q-1)S
n=nq
n-(1+q+q
2+……+q
n-1)
=nq
n-
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于是S
n=
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若q=1,則S
n=1+2+3+……+n=
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所以,S
n=
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……………………………………14分
點(diǎn)評:(1)若一個(gè)數(shù)列是等差數(shù)列和等比數(shù)列的乘積的形式,求其前n項(xiàng)和通常用錯(cuò)位相減法。(2)注意等比數(shù)列前n項(xiàng)和的形式:
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,注意對
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的討論。
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科目:高中數(shù)學(xué)
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①
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是數(shù)列
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的前
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項(xiàng)和,若
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,則
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③已知函數(shù)
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,若存在
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,使得
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成立,則
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④在
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中,
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則
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科目:高中數(shù)學(xué)
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(本題12分)
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
,等差數(shù)列
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滿足
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,
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。
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、

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,數(shù)列
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的前
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項(xiàng)和為
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>

的最小正整數(shù)
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
,
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,

,……,

的“理想數(shù)”為2004,那么數(shù)列2,
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,
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,……,
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的“理想數(shù)”為( )
A.2002 | B.2004 | C.2006 | D.2008 |
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(本小題滿分l0分) 在等比數(shù)列
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中,已知

.

求數(shù)列

的通項(xiàng)公式;

設(shè)數(shù)列

的前n項(xiàng)和為

,求
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(本小題滿分12分) 已知數(shù)列

為等差數(shù)列,且

,

.
(1) 求數(shù)列

的通項(xiàng)公式; (2) 令

,求證:數(shù)列
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是等比數(shù)列.
(3)令
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,求數(shù)列

的前
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項(xiàng)和

.
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設(shè)
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是等差數(shù)列{an}的前n項(xiàng)和,

,則
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的值為( )
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設(shè)

是等差數(shù)列


的前
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項(xiàng)和,且
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
,則
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=
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設(shè)等差數(shù)列
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的前
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項(xiàng)和為

,若
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,則
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=
。
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