已知函数
,若存在常数
,对任意
都有
,则称函数
为T倍周期函数.
(1)判断
是否是T倍周期函数,并说明理由;
(2)证明
是T倍周期函数,且T的值是唯一的;
(3)若
是2倍周期函数,
,
,
表示
的前n项和,
,若
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d298874d6f3f970df11a2969e8a6b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d2627f43a3c5cb52491fea5ef27b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f3ebbaf472c0ff1db137b6cf7b8f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a420e2cb3bf5011ea2516d3ea195681a.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ba9867a86c9ac7b2af229c4a768745.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263dae91fccf4f8f5778724c1f746e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737818f97b6740bb592d0231b89a1810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdf8cb6087b7fb3bb460bfb1cd58aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b3e1b506e10f0333dea0fb43eaab02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b952c6c21049d3c8b292c9078f0b7e2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a57f85ce74866d6fecc1892f18e817.png)
2016·上海杨浦·一模 查看更多[2]
更新时间:2020-02-02 09:25:59
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解答题-问答题
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名校
【推荐1】已知数列
是各项均不为
的等差数列,公差为
,
为其前
项和,且满足
,
.数列
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,
为数列
的前n项和.
(1)求数列
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的前n项和
;
(2)若对任意的
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,使得
成等比数列?若存在,求出所有
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c39dd748533f2afe8b5491460c3d42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b99375c025c8a57abd7595a0184e429.png)
![](https://img.xkw.com/dksih/QBM/2012/3/29/1570822592405504/1570822597566464/STEM/2e834399303b4f90932833e0dc4bf128.png)
(3)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77fde8c4aced29ce6b664d54ac95f87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa9480fca9e4b0389d69c90e9929a1d.png)
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解答题-证明题
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较难
(0.4)
【推荐2】已知数列
中,
,
,
(I)求证数列
是等差数列;
(II)试比较
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(III)求正整数
,使得对于任意的正整数
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f1defb2fa5a0c56b4fde73df2c6b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec50822b0ccaa19ccf643094817f6c8c.png)
(I)求证数列
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(II)试比较
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92a6c94a463d1d7dcb2e95647f96040.png)
(III)求正整数
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解答题-问答题
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(0.4)
名校
解题方法
【推荐1】对于数列
,若存在正数
,使得对任意
,
,都满足
,则称数列
符合“
条件”.
(1)试判断公差为2的等差数列
是否符合“
条件”?
(2)若首项为1,公比为
的正项等比数列
符合“
条件”.求
的范围;
(3)在(2)的条件下,记数列
的前
项和为
,证明:存在正数
,使得数列
符合“
条件”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04c7ba0ffd54e60b2829f4440c91ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
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(1)试判断公差为2的等差数列
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(2)若首项为1,公比为
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd07cd3600f1b5ab12e079890630edcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)在(2)的条件下,记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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您最近一年使用:0次
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解题方法
【推荐2】已知等差数列
的首项为
,公差为
,前n项和为
,且满足
,
.
(1)证明
;
(2)若
,
,当且仅当
时,
取得最小值,求首项
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532f0b684d80fa42ac32ca5d1a770424.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893e54804c54e9c1d1b68d302c9ffcaa.png)
(2)若
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您最近一年使用:0次