1 . 已知数列
满足
.
(1)当
时,求证:数列
不可能是常数列;
(2)若
,求数列
的前
项的和;
(3)当
时,令
,判断对任意
,
是否为正整数,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29f02a0752b4cc8301b7ea7bea8ac4b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda6dc559d07bc22c9a0ed1e3a6d01d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2385f5c338bb07f5aa51c85c39e412e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443c2a6dedb41dcc92b3a1cf6ffb82e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff6c3ddda021f541cd0a112574768db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adfd5a27fa743a41ae4e1d8672e7a647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
2021-12-21更新
|
1143次组卷
|
4卷引用:数学-2022年高考押题预测卷03(上海专用)
22-23高三上·北京房山·开学考试
解题方法
2 . 设
和
是两个等差数列,记
,其中
表示
这
个数中最小的数.
(1)若
,
,求
的值;
(2)若
,
,证明
是等差数列;
(3)证明:或者对任意实数
,存在正整数
,当
时,
;或者存在正整数
,使得
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec5456cafab2bd861b17181ac14f70e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b843e0dc4116c34c56f0c92c8c7ccd6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb05531d4fd9e4c4926c18b427ce090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf6e05fd55462f9c5acca3cf6ee46e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfd5bf623242a22364d6fb33731cf7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900b1d4f3f32b401c8e3d788df7035b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a08cafcb17e29f58f496c92a53df3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae491c2bb3517ac6b65745870b500636.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fd15570bcd1cc1228fd3929a7c3f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
(3)证明:或者对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8b754f5002b4db372cc622c99252c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75942dc6020cdaef88c28a9a077e5b08.png)
您最近一年使用:0次
3 . 已知无穷数列{an},对于m∈N*,若{an}同时满足以下三个条件,则称数列{an}具有性质P(m).
条件①:an>0(n=1,2,…);
条件②:存在常数T>0,使得an≤T(n=1,2,…);
条件③:an+an+1=man+2(n=1,2,…).
(1)若an=5+4![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
(n=1,2,…),且数列{an}具有性质P(m),直接写出m的值和一个T的值;
(2)是否存在具有性质P(1)的数列{an}?若存在,求数列{an}的通项公式;若不存在,说明理由;
(3)设数列{an}具有性质P(m),且各项均为正整数,求数列{an}的通项公式.
条件①:an>0(n=1,2,…);
条件②:存在常数T>0,使得an≤T(n=1,2,…);
条件③:an+an+1=man+2(n=1,2,…).
(1)若an=5+4
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cba79639deae5f8af6088b30c1a800.png)
(2)是否存在具有性质P(1)的数列{an}?若存在,求数列{an}的通项公式;若不存在,说明理由;
(3)设数列{an}具有性质P(m),且各项均为正整数,求数列{an}的通项公式.
您最近一年使用:0次
2021-05-02更新
|
1166次组卷
|
5卷引用:北京卷专题18数列(解答题)
4 . 若数列
满足
,则称数列
为“k阶相消数列”.已知“2阶相消数列”
的通项公式为
,记
,
,
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
___________ 时,
取得最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c925173742af19a056499a937c1db67.png)
![](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/71531020725584254a1fc8f1e55fccf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900212a9119d3ea0388504cab074c47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530c4defbccdf183003db56cc71e9c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
5 . 设数列
的前
项和为
,对一切
,点
都在函数
的图像上.
(1)将数列
依次按1项、2项、3项、4项循环地分为
、
、
、
、
、
、
、
、
、…,分别计算各个括号内各数之和,设由这些和按原来括号的前后顺序构成新的数列为
,求
的值;
(2)设
为数列
的前
项积,若不等式
对一切
都成立,求
的取值范围.
![](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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e6e0e0522300b27c59ea1920a7b725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc15b8864ee2c70e75b70684b7a2b5e.png)
(1)将数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b216d768026fa703c4a84ae2a8df0449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f083a6f04943110c24d0add2757bc501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8fe375194804d7482ff4403790d6a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc03993fe8538b814101c933896c5e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0449a2f9b428ce24935c4b11d1b71a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd71c79c25de550c3a1d84e65c18f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c4f28ba6dfb178034ed7eded576f29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14fe365cd7f9f94dcbd53750639530e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151f4f1a38fa5f79551b1d9c5d228e12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cf41b06e34f87048496c44e744acac.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09953c3d3c8bb8566bb740c3a7d53e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b188c0a43e179bc98660b000ab55d7fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
6 . 已知数列
:
,其中
,且
.
若数列
满足
,当
时,
或
,则称
:
为数列
的“紧数列”.
例如,数列
:2,4,6,8的所有“紧数列”为2,3,5,8;2,3,7,8;2,5,5,8;2,5,7,8.
(1)直接写出数列A:1,3,6,7,8的所有“紧数列”
;
(2)已知数列A满足:
,
,若数列A的所有“紧数列”
均为递增数列,求证:所有符合条件的数列A的个数为
;
(3)已知数列A满足:
,
,对于数列A的一个“紧数列”
,定义集合
,如果对任意
,都有
,那么称
为数列A的“强紧数列”.若数列A存在“强紧数列”,求
的最小值.(用关于N的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c68d4ed9e75f2cd7dd4382fd84f378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14386d3ebe0a13abcc6c57cac5da562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d291f70ac12e8eda5043e237872f40ab.png)
若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77307c2329739824dc4ebb00ce2f6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817668f6b387152a58a59af8120d0cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e685d8f0acaf70f65419c2f7254fb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5761e201b1c22ecdb526a1799a3f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6629b3737b2c34e2bfd2228d3dba8ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532fbe9e311f4e80e72ce9c058547017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95df0e3c85670e818483fe707483cf3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
例如,数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)直接写出数列A:1,3,6,7,8的所有“紧数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9f1f859a3544dd1990cc3931cd7682.png)
(2)已知数列A满足:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade9b6affad439cb8de5b1d81a3de498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9f1f859a3544dd1990cc3931cd7682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945f4f3bbb203dbcab32cdb5a857b468.png)
(3)已知数列A满足:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9f1f859a3544dd1990cc3931cd7682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79dadf52c07bd746cbd9528513ddf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28171a8e884a41b26c7da8fc1185b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59a038b683412a470a6aac203e12ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9f1f859a3544dd1990cc3931cd7682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
您最近一年使用:0次
2022-12-06更新
|
582次组卷
|
5卷引用:数学(北京B卷)
7 . 已知数列
,具有性质P:对任意
(
)
与
,两数中至少有一个是该数列中的一项,
为数列
的前
项和.
(1)分别判断数列0,1,3,5与数列0,2,4,6是否具有性质P:
(2)证明:
且
;
(3)证明:当
时,
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab0618ddda6e7eeba8a14c2655833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb18c6dbf63138dd5cf7cae946c106e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae331839bce8f3c14d7efd7f9d8915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)分别判断数列0,1,3,5与数列0,2,4,6是否具有性质P:
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1fe4c51169a32e05e4be4acb3d1f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc31cec2f263c4fbed39962f960daef.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd49c085be2656091b79da53f010a1a.png)
您最近一年使用:0次
2021-03-25更新
|
947次组卷
|
3卷引用:考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮
名校
解题方法
8 . 已知数列
的前
项和为
,且满足
,
,设
,
.
(Ⅰ)求证:数列
是等比数列;
(Ⅱ)若
,
,求实数
的最小值;
(Ⅲ)当
时,给出一个新数列
,其中
,设这个新数列的前
项和为
,若
可以写成
(
,
且
,
)的形式,则称
为“指数型和”.问
中的项是否存在“指数型和”,若存在,求出所有“指数型和”;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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22afec8bdc08ff937a2f386d95e9f1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad47c46bcf213c73471655c08c53e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b73fd5c8507824f28ee1569ae5fad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(Ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbb71aacea5a3e019c3d081428834f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c340d7d093dd4a275ffea4b87cd26827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d4dea64b7e8e597c1601d4340c7f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98432c54bd7df6e5e6a425f9ec04218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6a22128f7e9de6fb6c0edf38c3d2e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544530e1133b2924ccfbe691141a5641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dab9e79198239cda875305fd6809b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ef8539a7a09303a95b4e79fb9949fc.png)
您最近一年使用:0次
2020-03-24更新
|
1264次组卷
|
6卷引用:专题10 数列通项公式的求法 微点1 观察法(不完全归纳法)、公式法
(已下线)专题10 数列通项公式的求法 微点1 观察法(不完全归纳法)、公式法2015届北京市东城区高三5月综合练习二理科数学试卷北京市陈经纶中学2019-2020学年第一学期高二数学期中试题上海市浦东新区建平中学2019-2020学年高三下学期(4月)模拟数学试题2020届上海市高三高考压轴卷数学试题上海市2022届高三模拟(三)数学试题
9 . 定义圈数列X:
;X为一个非负整数数列,且规定
的下一项为
,记
,这样
的相邻两项可以统一表示为
(
的相邻两项为
,即
;
的相邻两项为
).定义圈数列X做了一次P运算:选取一项
,将圈数列X变为圈数列
:
,即将
减2,相邻两项各加1,其余项不变.并记下标k输出了一次.记X进行过i次P运算后数列为
:
(规定
)
(1)若X:4,0,0,直接写出一组可能的
;
(2)若进行q次P运算后
,有
,此时下标k输出的总次数为
,记
直接写出一组非负实数
,使得
对任意
,都成立,并证明
;
(3)若X:
,0,0,…,0,证明:存在M,当正整数
时,
中至少有一半的项非零.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f214157de400b0b2a1e05537099f923d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87907959756f00396669363cf88eaf08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b1c7fa6b6f144a64d74919d10850df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bbd725411153f3633f4890fbfaa660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0894405d04b1d2a5cfad77ff782676fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e749b2d939983c253168c181d1da75b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d21eab854a007f760b8a1c10111bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa838b409a2f7e7116597f76df30c2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221d51ced11c126b1b3e90806fd68ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0669b68e68a3ae7514cef46c1dfaaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63bde043b466cec4c2edc08e56fc9af9.png)
(1)若X:4,0,0,直接写出一组可能的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b753f542ea6fcf63c231f3408e474421.png)
(2)若进行q次P运算后
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de57e05208fa589f2bf2033d80765d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9123a44524ca34d63b0b70122b0d41ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5a77c83f6b7cb83300b70b09436339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1684f90061da517e8825e791a5a06b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1779444296713b01857e045cdda2d08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6efdcc42efa52de9ab2c7a707c4ad4.png)
(3)若X:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208575de4f7422c995dd601c54d264d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9cce113f874ea096ee027d0c7d2ad27.png)
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2022-12-31更新
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4卷引用:2020年高考北京数学高考真题变式题16-21题
(已下线)2020年高考北京数学高考真题变式题16-21题北京市北京大学附属中学2022届高三12月月考数学试题北京市人大附中2022届高三上学期数学收官考试之期末模拟试题北京市第二中学2023届高三下学期开学测试数学试题
10 . 已知
,有穷数列
满足
,将所有项之和为
的可能的不同数列
的个数记为
.
(1)求
,
;
(2)已知
,
,若
时,总有
,求出一组实数对
;
(3)求
关于
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6715f4300d689fe5d01d681b7d91b902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f792b089573cec34e01c18a74eb9b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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