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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12分)
設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710448456.png)
是等差數(shù)列,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710464471.png)
是各項(xiàng)都為正數(shù)的等比數(shù)列,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710479487.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710526610.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710542613.png)
(Ⅰ)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710448456.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710464471.png)
的通項(xiàng)公式;
(Ⅱ)求數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710588681.png)
的前
n項(xiàng)和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004710620388.png)
.
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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15分)
數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824000302655481.png)
是首項(xiàng)為23,公差為整數(shù)的等差數(shù)列,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824000302655447.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824000302687435.png)
.
求:(1)數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824000302655481.png)
的公差;
(2)前
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824000302718297.png)
項(xiàng)和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824000302733388.png)
的最大值;
(3)當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824000302765499.png)
時(shí),求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824000302718297.png)
的最大值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234547765776.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234547796518.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234547812277.png)
的最小值為 ( )
A.6 | B.![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234547828254.png) | C. 8 | D.9 |
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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12分)數(shù)列{a
n}滿足a
1=1,a
n=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823234018620338.png)
a
n-1+1 (n≥2)
⑴ 寫出數(shù)列{a
n}的前5項(xiàng);
⑵ 求數(shù)列{a
n}的通項(xiàng)公式。
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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
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905393390.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905408431.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905424455.png)
,……,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905439785.png)
,……
(1)計(jì)算
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905455342.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905486374.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905517377.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905595364.png)
(2)根據(jù)(1)中的計(jì)算結(jié)果,猜想
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823231905627388.png)
的表達(dá)式并用數(shù)學(xué)歸納法證明你的猜想。
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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12分)
已知數(shù)列{a
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234283240.png)
}的前n項(xiàng)和Sn= —a
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234283240.png)
—(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234329338.png)
)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234345292.png)
+2 (n為正整數(shù)).
(1)證明:a
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234376306.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234329338.png)
a
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234283240.png)
+ (
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234329338.png)
)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234454305.png)
.,并求數(shù)列{a
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234283240.png)
}的通項(xiàng)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234501511.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234517469.png)
,T
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234283240.png)
= c
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234563195.png)
+c
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234595240.png)
+···+c
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234283240.png)
,求T
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823223234626250.png)
.
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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13分)
已知f(x)=m
x(m為常數(shù),m>0且m≠1).
設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823204253941158.png)
f(a
1),f(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823204253957164.png)
a
2),…,f(a
n)…(n∈N
?)是首項(xiàng)為m
2,公比為m的等比數(shù)列.
(1)求證:數(shù)列{a
n}是等差數(shù)列;
(2)若b
n=a
n·f(a
n),且數(shù)列{b
n}的前n項(xiàng)和為S
n,當(dāng)m=2時(shí),求S
n;
(3)若c
n=f(a
n)lgf(a
n),問是否存在m,使得數(shù)列{c
n}中每一項(xiàng)恒小于它后面的項(xiàng)?若存在,
求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823204253973161.png)
出m的范圍;若不存在,請說明理由.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212047957494.png)
的通項(xiàng)公式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823212047973726.png)
,則該數(shù)列的前( )項(xiàng)之和等于
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