1 . 已知数列
满足
,
.
(1)若
是递增数列,求实数
的取值范围;
(2)若
,且对任意大于
的正整数
,恒有
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d0b399e3826e2721d683a357fe5dd4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e144b442dc601367909266594699b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaacfaef44a654c0a1c283ef03fc0550.png)
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2 . 若正整数
的二进制表示是
,这里
(
),称有穷数列1,
,
,
,
为
的生成数列,设
是一个给定的实数,称
为
的生成数.
(1)求
的生成数列的项数;
(2)求由
的生成数列
,
,
,
的前
项的和
(用
、
表示);
(3)若实数
满足
,证明:存在无穷多个正整数
,使得不存在正整数
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a573743c22f1988094a801651af5611e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1065440ee09654f97b50b5ef6a963ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef7fb812f8cb384ae86e75fb949ac66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30de4943aa77db7dc0b92b29b2aa93f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208400bfcdb85a19359c14f2c66e17c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fde3541708c770e48a06c28f9a3434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf09398436b9b00458c5d9b245ba287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c15a081508b98e5c53ebedc4be56c45.png)
(2)求由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b51c3c1cbed76bbb68d50f7df7209a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45c1e00ea3205d39449f3f9d64ec126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa7f3694402a60c3b50e39a76d87c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a28b156b7cb863056fda24d66fff68.png)
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3 . (1)证明:
(
且
);
(2)证明:对一切正整数
和一切实数
,
,
,
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092d5cf7ee736195147eed7aedf84d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85319a950bf16b9388aa81a5b36b67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870c36161f465fc992534b5fc3777f3.png)
(2)证明:对一切正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea675d7b6c3299771619fabfca45789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361baf932d588dd0dc6f771df392c553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0abcce93ef419ad1eaa9fa278d6db4.png)
您最近一年使用:0次
2020-07-17更新
|
1050次组卷
|
4卷引用:江苏省连云港市赣榆区2020届高三(6月份)高考数学仿真训练试题
江苏省连云港市赣榆区2020届高三(6月份)高考数学仿真训练试题(已下线)考点34 排列、组合(练习)-2021年高考数学复习一轮复习笔记江苏省南通市如皋中学2020届高三创新班下学期高考冲刺模拟(四)数学试题(已下线)对点练68 排列与组合-2020-2021年新高考高中数学一轮复习对点练
4 . 对一切自然数
,猜出使
成立的最小自然数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c067f303c08497a38297ae0bb56246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
您最近一年使用:0次
5 . 设
,以
表示正整数b,c的最小公倍数.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27234e2e7b22e5c1bdd8a7a221d9d7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e682f89425146ac9cb16b2f13a014c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9197cd1f45fdd9415fc4e2d65915ddcd.png)
您最近一年使用:0次
6 . 若数列
满足
,
,则使得
的正整数
的数目为( )个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb93df462dde10cc60418cbccaaeb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c8d0474f7d81ef8dbefaacfd5afe7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea53c334b2d633d73489f95cd4e57841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596f7c59b0df339616870dde35061191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.0 | B.1 | C.2 | D.大于2 |
您最近一年使用:0次
7 . 已知数列
满足:
,若对任意正整数
,都有
,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c568e405619a4623bffcd8a03dab37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76ca08fb2d8577f0b0e5b16e5c98693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 已知数列
满足:
,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f75723824158fae6941098197f51b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d996de3c21f0fbec3750b1985fc6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b871ed324a95d6c6daf03fda30feb9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d39d6aa1813347686313bc667026d52.png)
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9 . 求最小的正整数
,使得当正整数点
时,在前
个正整数构成的集合
中,对任意
总存在另一个数
且
,满足
为平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2ba3c51d2726df8cee0918b8af2d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc6a0568db5a3fc7aca3366e608cf69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7580ce638933a1c81da5e2e1b656c77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7741c8d8f0486556a102d904fb26a7be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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10 . 设
为非负数,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ef6a16ec8802b2271d1e4d5cf87c6f.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ef6a16ec8802b2271d1e4d5cf87c6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d3aeb20017d60244b090bb862f4b62.png)
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