在数列
中,
,则使
对任意的
恒成立的
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709500a091cba79169e10b2ba381a3cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3514b5724d8d5a9fdb69a3558038d214.png)
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22-23高二下·云南·阶段练习 查看更多[4]
云南省部分名校2022-2023学年高二下学期3月大联考数学试题(已下线)第83练 计算速度训练3(已下线)4.1 等差数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)【练】专题5 分段数列问题
更新时间:2023-03-27 13:17:45
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【推荐1】十九世纪法国数学家卢卡斯提出数列
:2,1,3,4,7,…,称之为卢卡斯数列,且满足
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e60fae499371b1a4de8ef6589276e4d.png)
________ ;记
为数列
的前
项和,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78d551e6cc415f570dc7fc49b825cb1.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a31ef624a37474c9ff6055483e0692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ea0943c8abc65344516556368c4eb.png)
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【推荐2】①在
中,若
,
,
,则此三角形的解的情况是两解.
②数列
满足
,
,则
.
③在
中,
为中线
上的一个动点,若
,则
的最小值是
.
④已知
,则
.
⑤已知等比数列
的前
项和为
,则
,
,
成等比数列.
以上命题正确的有______ (只填序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a110bb6e761a161260c92dea2121d2db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f48934086667319958726544e37f649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54a36173cd9b7b28e91619d715cb569.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9f5746a7728ce4aa2557d1269ffb37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeaa7871bcc1c45c752895d535e907ce.png)
③在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810fee760e06028fb7d37e65db79bfa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f0d68fb700d93bb711ab383bc0df71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886f3c1fc76321833d2a8dd8f1a0b707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b27502c1bb8e01c37fa5a72853814c.png)
⑤已知等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5188d6760683a860adab0cda195cdf80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd6fe11dfa538e67bfd63478fc428a1.png)
以上命题正确的有
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解题方法
【推荐1】各项均为正数的数列
和
满足:
,
,
成等差数列,
,
,
成等比数列,且
,
,则数列
的通项公式为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
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【推荐2】已知数列
满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
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