已知数列
满足
.
(1)求证:
.
(2)是否存在实数
,使得
,若存在求出
的值;若不存在.请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dffe4a726c5d5c2c1b51255dd6e9015.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41ebd083ba2fdca7e830d62e3d5181b.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0920804135bf9f7a222df640a6e874ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
2021高三·全国·竞赛 查看更多[1]
更新时间:2021-07-21 19:46:10
|
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较难
(0.4)
【推荐1】设正数数列
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39310acb3c9b3cf6190f87b26364fd2a.png)
(
=3,4,
,
)且
,
.
(1)求
,
,
;
(2)证明
,
,
,
是自然数列,即
. (
=1,2,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fb97888c923a843a3b4806d3fd0733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39310acb3c9b3cf6190f87b26364fd2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ad6b84eabbce9f623343dca91ae7e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ba808c24aeae6a2f34b98ae5ec04ae.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea867f78d52b7382c38e8fc6e2e2a9c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323853b2985c46b7f2611eea2af92786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f059f0b942a8658ca91eb2217ec4f26f.png)
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【推荐1】圆周上分布着2002 个点,现将它们任意地染成白色或黑色,如果从某一点开始,依任一方向绕圆周运动到任一点,所经过的(包括该点本身)白点总数恒大于黑点总数,则称该点为好点.为确保圆周上至少有一个好点,试求所染黑点数目的最大值.
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【推荐2】给定正整数
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中的任意两个集合至多有一个公共元素;
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试求
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ee628911994243c46467361fd30098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950b2b2d555ce0f0adbdb85a63b30778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a279eed3fea6a07ffc2e7784b9dfcfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a279eed3fea6a07ffc2e7784b9dfcfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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