名校
1 . 已知数列
满足:
①对任意质数p和自然数n,都
;
②对任意互质的正整数对
,都有
.
(1)写出
的前6项,观察并直接写出
与能整除n的正整数的个数的关系
;
(2)设数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①对任意质数p和自然数n,都
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c13d00316b2eccfec8ac0bca0cac355.png)
②对任意互质的正整数对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/514fbceb6c0ae220d85df10009ed9fed.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2889dd3096379db5dfdd51305bdbb743.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60de6c5fd063c2e26d12d43aa13eac8c.png)
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名校
2 . 已知数列
的前
项和为
且
,
.
(1)求证
为等比数列,并求出数列
的通项公式;
(2)设数列
的前
项和为
,是否存在正整数
,对任意
,不等式
恒成立?若存在,求出
的最小值,若不存在,请说明理由.
![](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/8d7a9511c3d1b6d41d17df1559919880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e8adbe4d237aa33ca4d24901df8cfcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b93708dc68d1509f7030bdf7918bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad83668ff336589f82a2cd04db9f9947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04c7ba0ffd54e60b2829f4440c91ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae1d8b82b6b00c861167fa7c3a796c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2017-10-09更新
|
2403次组卷
|
4卷引用:湖北省潜江市城南中学2018届高三期中考试 文科数学试题
3 . 已知数列
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694d9d408cec688e8c8a13e4868a5deb.png)
(I)求证:数列
是等比数列
(II)求数列
的通项公式
(III)设
,若
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694d9d408cec688e8c8a13e4868a5deb.png)
(I)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6631307e8ff61b215f447f2527c36e04.png)
(II)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(III)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9dfeeff5b7c543226a16dac4509375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23487d83aa14650649f1e0b636acabb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6143b63cb006d60ffb578a90da8f9f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2017-12-11更新
|
3794次组卷
|
11卷引用:湖北省黄冈市黄梅国际育才高级中学2019-2020学年高一下学期复学考试数学试题
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真题
4 . 设n是正整数,r为正有理数.
(1)求函数f(x)=(1+x)r+1﹣(r+1)x﹣1(x>﹣1)的最小值;
(2)证明:
;
(3)设x∈R,记[x]为不小于x的最小整数,例如
.令
的值.
(参考数据:
.
(1)求函数f(x)=(1+x)r+1﹣(r+1)x﹣1(x>﹣1)的最小值;
(2)证明:
![](https://img.xkw.com/dksih/QBM/2014/5/22/1571735197384704/1571735202652160/STEM/b210b038fbb344ac94a54aec26f9c0b2.png)
(3)设x∈R,记[x]为不小于x的最小整数,例如
![](https://img.xkw.com/dksih/QBM/2014/5/22/1571735197384704/1571735202652160/STEM/5941330c7eba43a5b07a8f3fbdc39e10.png)
![](https://img.xkw.com/dksih/QBM/2014/5/22/1571735197384704/1571735202652160/STEM/108a733b55f84c2e9e222d7a48ca2ca8.png)
(参考数据:
![](https://img.xkw.com/dksih/QBM/2014/5/22/1571735197384704/1571735202652160/STEM/2c1b4efceba3424a99b79389879110ff.png)
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