1 . 已知数列
的各项均为正整数,记集合
的元素个数为
.
(1)若
为1,2,3,6,写出集合
,并求
的值;
(2)若
为1,3,a,b,且
,求
和集合
;
(3)若
是递增数列,且项数为
,证明:“
”的充要条件是“
为等比数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c540d73bfd5449a65bd3938606a734e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9721608a6a8893ab6ed39687ea3c5cc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9721608a6a8893ab6ed39687ea3c5cc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e068e11427f0179d2233862d835b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87ced0211b3e32adbaae957c084973e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2 . 若数列
在某项之后的所有项均为一常数,则称
是“最终常数列”.已知对任意
,函数
和数列
满足
.
(1)当
时,证明:
是“最终常数列”;
(2)设数列
满足
,对任意正整数
.若方程
无实根,证明:
不是“最终常数列”的充要条件是:对任意正整数
,
;
(3)若
不是“最终常数列”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc6de641322c6aeb24e0bbd875e65b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3980f4d5c5ec0f551d7a3c3c0b5ffdc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b26218ecae19cc13017d561c01d69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36737370e7f4231ebdd27c957f47f45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8f2cc86844dc647bfb33344781e75a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c77ea288be5bfb4445a76a2429aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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3 . 当
时,定义运算
:当
时,
;当
时,
;当
或
时,
;当
时,
;当
时,
.
(1)计算
;
(2)证明,“
或
”是“
”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b8043346a0a80781b0d9a7c9cecd4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e16415b61722f9961e412386e6819f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28f616b1f56991ee75caae3ac35208b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a05cb3647f1ad81e328f8379b51291b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6910a71dc1e164c35b110ad0d68e3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9e3cf30d7a15408ddd0697a1fcf3d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4aa46e2bdec36770ee57fe67639ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4581917005539a0806619080496676e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85349216e2fbdaa860e9f81b3924af3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987270ce2ca977277b0a3d13cb20a9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb01e9ee38d5b6ab84c19789cb5af195.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a26d77e8c7e6ffc9ea9b9ed6d813a1.png)
(2)证明,“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d05a5b738133c7204d1c8f90e30ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfc50db0551c95ea1c63550750db33b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ffb9194dead5975e453628f5bac1e7.png)
您最近一年使用:0次
21-22高一·湖南·课后作业
4 . 求证:
对任意实数
,
,
,
成立,等号成立的充分必要条件
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d115a39e93fabee911c86269199e13d0.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/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9490b6aa3c70b2d602ee98369f5aede.png)
您最近一年使用:0次
名校
5 . 设
,求证:“
是偶数”是“
是奇数”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f02d5c8eec434a3f90348d770a2e2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00470075ebfa218745e54f7521ba839.png)
您最近一年使用:0次