1 . 若数列
满足
(
,且
为实常数),
,则称数列
为
数列.
(1)若数列
的前三项依次为
,
,
,且
为
数列,求实数
的取值范围;
(2)已知
是公比为
的等比数列,且
,记
.若存在数列
为
数列,使得
成立,求实数
的取值范围;
(3)记无穷等差数列
的首项为
,公差为
,证明:“
”是“
为
数列”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a308a3e9b4cbfaebc891850bca6d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8047f0a8bd0cf4e250cd0fe80093b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a70994adb16e3b90738c1130ca21113.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1222cf2ecfe85c078a3c192fc3f02ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37933cfc60b4bd29f1684687ddd2cbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e954ddd309b0adf31b3627db0d8f7d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fde3541708c770e48a06c28f9a3434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a9dc9d42849a5b67043241e0f04d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ce32f902c54d9540d0755acb252d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e5ac20cde9cb0eec8853f409afcfe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)记无穷等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89087b3022c9011d7ddf9ade06d137e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a70994adb16e3b90738c1130ca21113.png)
您最近一年使用:0次
2020-12-25更新
|
461次组卷
|
3卷引用:考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)
2 . 对于数列
:
,
,
(
,
),定义“
变换”:
将数列
变换成数列
:
,
,
,其中
(
),且
.这种
变换“记作
.
继续对数列
进行“
变换”,得到数列
:
,
,
,依此类推,当得到的数列各项均为0时变换结束.
(1)试问
:2,6,4经过不断的“
变换”能否结束?若能,请依次写出经过“
变换”得到的各数列;若不能,说明理由;
(2)设
:
,
,
,
.若
:
,2,
(
),且
的各项之和为2012.求
,
;
(3)在(2)的条件下,若数列
再经过
次“
变换”得到的数列各项之和最小,求
的最小值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30e41720595d1f4d83a77514980f9f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79059a3366ed1b339ba1317ce8a1e7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1db52d417ef7dd57eeb2cf1ff03f079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd74add83d098d62539e2d8234e2d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e374762fa02d95091036d3d4df4e590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6cbe989475017c34c79eadde5fb93f9.png)
继续对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
(1)试问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6cbe989475017c34c79eadde5fb93f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1132de2e8913dba9c5cc2396ecb09fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在(2)的条件下,若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2021-10-12更新
|
347次组卷
|
4卷引用:考向29 推理与证明-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向29 推理与证明-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)数学-2022年高考押题预测卷01(上海专用)上海市2022届高三上学期一模暨春考模拟卷(一)数学试题上海市南洋模范中学2020届高三下学期4月月考数学试题
真题
名校
3 . 记
为不超过实数
的最大整数,例如,
,
,
.设
为正整数,数列
满足
,
,现有下列命题:
①当
时,数列
的前3项依次为5,3,2;
②对数列
都存在正整数
,当
时总有
;
③当
时,
;
④对某个正整数
,若
,则
.
其中的真命题有____________ .(写出所有真命题的编号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443b8dbfd8fa228f091e8c1d8910f705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e935bb66ce8ce69c0a4043aa5c820a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd905e6eeb729a6135b8d9b49c1af50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c4cdcb32e3a0ce527c13978c022a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa28b7a64fcb7d2714c20cbd0006648.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab839d8569171afab5ed55c22013aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
②对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fef5f2a4235817fb704d29e08766e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28eb741935c8eaaaeb8fa68f674ee10b.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd0de9946f770bdc7202847a035c05f.png)
④对某个正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96091e4ba6af0daa2324031ab74e7431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f88564d9154ce9deac6650a05a1c56.png)
其中的真命题有
您最近一年使用:0次
2016-12-01更新
|
2329次组卷
|
3卷引用:考向18 数列不等式-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向18 数列不等式-备战2022年高考数学一轮复习考点微专题(上海专用)2012年全国普通高等学校招生统一考试理科数学(四川卷)北京师范大学第二附属中学2023解高三上学期期中考试数学试题
名校
4 . 已知项数为
的数列
为递增数列,且满足
,若
,且
,则称
为
的“伴随数列”.
(1)数列
是否存在“伴随数列”,若存在,写出其“伴随数列”若不存在,请说明理由;
(2)若
为
的“伴随数列",证明:
;
(3)已知数列
存在“伴随数列
,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982af54633665d2ce880c1ddffa5f557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad1fbb3a6370e293d2908eb3e054de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2444587892c098c2d64c3b96db6e1897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ebc5304d7aac9ffbbbd0f0b91d3daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4660fd74b3f3df8036e78d59fab2f637.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f74bd1b8f7484f22f4b09fe9de24986.png)
(3)已知数列
![](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/e934e1623c0064db4ab5cfcf1ac706be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
5 . 已知数列
满足:对任意
,若
,则
,且
,设
,集合
中元素的最小值记为
;集合
,集合
中元素最小值记为
.
(1)对于数列:
,求
,
;
(2)求证:
;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5897fd42e01b077fe8685e7b7a71e278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfbc054e041fa0b53feb9b81a4608347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7aad65e4222bcab9f6ddc94ea495de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f8fdbba79ddbc156bbb300b1b051e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74fd79d9aa9740d095affe36788e01cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a1493a001b60b0e94e342d428caa.png)
(1)对于数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3cf64aad412f59d047c97efa1516175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a1493a001b60b0e94e342d428caa.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aa00523d3ab546ab459d1fff0a6136.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
您最近一年使用:0次
2020-06-13更新
|
479次组卷
|
4卷引用:考向29 推理与证明-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向29 推理与证明-备战2022年高考数学一轮复习考点微专题(上海专用)2020届上海市七宝中学高三三模数学试题上海市七宝中学2020届高三下学期模拟数学试题(已下线)卷11-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)
2018·上海浦东新·三模
名校
6 . 设
,若无穷数列
满足:对所有整数
,都成立
,则称
“
-折叠数列”.
(1)求所有的实数
,使得通项公式为
的数列
是
-折叠数列;
(2)给定常数
,是否存在数列
,使得对所有
,
都是
-折叠数列,且
的各项中恰有
个不同的值?证明你的结论;
(3)设递增数列
满足
.已知如果对所有
,
都是
-折叠数列,则
的各项中至多只有
个不同的值,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98251cd3c3e36825493a3f83b0ac9d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cdd87bcc6088bea7dc1f24387b0502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)求所有的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6290fabfee064ca7296364c2011c16ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(2)给定常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270672a95f2a5349bc440c53b5dd4a12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbc76e88046029a006e48b6b58823d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbf39f278f6fcfbd30de4a1ad65e5bf.png)
(3)设递增数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818b2c2d51316638cf39039d6cb4d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74927b7593fd0b4f218b3806e3025dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b037996f28c91402cff9c883c99a8e6.png)
您最近一年使用:0次
7 . 一个有限数列
、
、
、
的部分和定义为
,其中
,称
为该有限数列的“凯森和”.已知一个有
项的数列
、
、
、
的“凯森和”为
,则有
项的数列
、
、
、
、
的“凯森和”为_______ .
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b917398953b08b03290a88e114d2209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7601dbefa6836756e3d2731b79af0126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ef7e1edfb70df79e5fc9945b0a200e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d477892dbc2e97c50c3a49eda36479.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4529b60c35db6356b49e6afa60168001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea0ed7fa8c4b56eb9994753e57d5166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070189e70ac29170817736a14f60f965.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4529b60c35db6356b49e6afa60168001.png)
您最近一年使用:0次
名校
8 . 对于无穷数列
的某一项
,若存在
,有
成立,则称
具有性质
.
(1)设
,若对任意的
,
都具有性质
,求
的最小值;
(2)设等差数列
的首项
,公差为
,前
项和为
,若对任意的
数列
中的项
都具有性质
,求实数
的取值范围;
(3)设数列
的首项
,当
时,存在
满足
,且此数列中恰有一项
不具有性质
,求此数列的前
项和的最大值和最小值以及取得最值时对应的
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0c73a1455fc61a2239cb62de1f3c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d08a34dcc16864fa2b14e4976353f6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834925e383a1e904951eea76b55bcb4f.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710bbca8506891a1063666a767c51f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834925e383a1e904951eea76b55bcb4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2815b24f5a89be7ae53aed93182e8988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019b05bea316a92cf1103e8c70bdbd6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0a9523f2084cf17b8656c11ab1d95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677dcea09d90af109df9cc72cff15cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(3)设数列
![](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/574f79bef0df7c026b0e7a6ec9de4a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea98988705ce9311cbad9e3b763f99cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc251c0f3be74183f20e70d65e5c8740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1caaa2fc4db5f4ac0829f53ffbe4c0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2020-07-06更新
|
431次组卷
|
4卷引用:2021年高考数学押题预测卷(上海专用)01
(已下线)2021年高考数学押题预测卷(上海专用)012020届上海市普陀区高三二模数学试题上海市普陀区2020届高三下学期质量调研数学试题上海市吴淞中学2023-2024学年高二上学期期末质量检测数学试卷
名校
9 . 音乐与数学有着密切的联系,我国春秋时期有个著名的“三分损益法”:以“宫”为基本音,“宫”经过一次“损”频率变为原来的
,得到“徵”;“徵”经过一次“益”,频率变为原来的
,得到“商”;……依次损益交替变化,获得了“宫、徵、商、羽、角”五个音阶,设“宫”的频率为
,则“角”的频率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
您最近一年使用:0次
2020-09-03更新
|
450次组卷
|
4卷引用:考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)课时25 数列新定义-2022年高考数学一轮复习小题多维练(上海专用)2020届上海市七宝中学高三高考押题卷数学试题沪教版(2020) 选修第一册 单元训练 第4章 等比数列(A卷)
名校
解题方法
10 . 已知数列
,若对任意
,都有
成立,则称数列
为“差增数列”.
(1)试判断数列
是否为“差增数列”,并说明理由;
(2)若数列
为“差增数列”,且
,
,对于给定的正整数m,当
,项数k的最大值为20时,求m的所有可能取值的集合;
(3)若数列
为“差增数列”,
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f42ca484ac17f08945a0d5560ee80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(1)试判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec340457210723f02b6088e997ae7ee.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b614e06663d93a618d95f416e35af54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e75ed912036a9003c90845863e148f.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547040beccf86047650dd0faebfc6636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f921d99e0b5e86b44cdb688a46829c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60074c9371ee5d12dc2dd5bbdbf92e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0a13ea2c9653a1a05612d85ab72a0b.png)
您最近一年使用:0次
2020-05-21更新
|
446次组卷
|
3卷引用:考向18 数列不等式-备战2022年高考数学一轮复习考点微专题(上海专用)