1 . 算前几项:
、
、
、
、
等各项的值,可以猜想:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e404b0333f773459318d0988deac20da.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ffd4c3b5803c304d3672e70769aa44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607c54043411245c03452809d28233fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf708eee8ff6bdeda03901db0119cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e404b0333f773459318d0988deac20da.png)
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解题方法
2 . 观察下面的解答过程:已知正实数a,b满足
,求
的最小值.
解:∵
,
∴
,
当且仅当
,结合
得
,
时等号成立,
∴
的最小值为
.
请类比以上方法,解决下面问题:
(1)已知正实数x,y满足
,求
的最小值;
(2)已知正实数x,y满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57f879f6e8df7d5fb261328806260b3.png)
解:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e312ceb0190fdd2b5481cc456417c2c.png)
当且仅当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c34bb88b7df81b0a9cc4f5f532f529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f86c800af77b70d7799500a45f91721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddab9f2cdfbb37f5d5845e7943910624.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57f879f6e8df7d5fb261328806260b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7e08b98c26303f2f61de7e7ddd2.png)
请类比以上方法,解决下面问题:
(1)已知正实数x,y满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08677c8308807e4dca6fd9410d301a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407e4330cfdd5cd0bcfd4f3bd1a898e6.png)
(2)已知正实数x,y满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d643ad258c07374425f3dfd3e07e1c.png)
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解题方法
3 . P为椭圆
上异于左右顶点
,
的任意一点,则直线
与
的斜率之积为定值
,将这个结论类比到双曲线,得出的结论为:P为双曲线
上异于左右顶点
,
的任意一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91c9bbbe71a1e6aa806b8a109fb52ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
A.直线![]() ![]() ![]() |
B.直线![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2022-04-28更新
|
395次组卷
|
5卷引用:天津市第一中学滨海学校2021-2022学年高二下学期4月复课摸底考试数学试题
天津市第一中学滨海学校2021-2022学年高二下学期4月复课摸底考试数学试题(已下线)第15讲 直线和圆锥曲线的位置关系-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)(已下线)3.3(附加3)圆锥曲线定点与定值问题-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)3.2.2 双曲线的几何性质(三) (同步练习提高篇)(已下线)重难专攻(九)?圆锥曲线中的定值问题 讲
4 . 如图,在谢宾斯基三角形中,
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963684015341568/2965072622477312/STEM/4408d978-e1f8-4e4f-821d-35f9b3a08f53.png?resizew=248)
(1)每个三角形中黑色小三角形的个数依次构成数列
,求
的通项公式;
(2)当
时,求在大黑色三角形内共去掉几个小三角形的个数.
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963684015341568/2965072622477312/STEM/4408d978-e1f8-4e4f-821d-35f9b3a08f53.png?resizew=248)
(1)每个三角形中黑色小三角形的个数依次构成数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
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名校
5 . 观察下面三个等式:
第1个:
,
第2个:
,
第3个:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21a4bed6c4709b97605bed530ffa84f2.png)
(1)按照以上各式的规律,写出第4个等式;
(2)按照以上各式的规律,猜想第
个等式(
为正整数);
(3)用数学归纳法证明你的猜想成立.
第1个:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50086dbfeae56333ce8863b59cb3aa07.png)
第2个:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4ba999165c5d5cb64b913580314bd1.png)
第3个:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21a4bed6c4709b97605bed530ffa84f2.png)
(1)按照以上各式的规律,写出第4个等式;
(2)按照以上各式的规律,猜想第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)用数学归纳法证明你的猜想成立.
您最近一年使用:0次
2022-04-24更新
|
313次组卷
|
5卷引用:沪教版(2020) 选修第一册 新课改一课一练 第4章 4.4.1 数学归纳法
沪教版(2020) 选修第一册 新课改一课一练 第4章 4.4.1 数学归纳法内蒙古包头市第六中学2022-2023学年高二上学期期末线上考试理科数学试题(已下线)4.4 数学归纳法(精讲)-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)(已下线)4.4 数学归纳法(6大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)(已下线)专题4.4 数学归纳法(2个考点四大题型)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)
6 . 观察下列等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27336f9955d622979463a6244b8bc631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e190ab298b89f85f5fe1951d2c82376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8e8b00b99009c2b401320f92966b0b.png)
……
据此规律,请你猜想出第
个等式并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27336f9955d622979463a6244b8bc631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e190ab298b89f85f5fe1951d2c82376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8e8b00b99009c2b401320f92966b0b.png)
……
据此规律,请你猜想出第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2022-04-24更新
|
135次组卷
|
5卷引用:沪教版(2020) 选修第一册 新课改一课一练 第4章 单元复习
沪教版(2020) 选修第一册 新课改一课一练 第4章 单元复习(已下线)第四章 数列(A卷·知识通关练) (4)(已下线)4.4 数学归纳法(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)(已下线)4.4 数学归纳法(2)1.4 数学归纳法(同步练习基础版)
7 . 有以下命题:设
,
,…
是公差为
的等差数列
中任意
项,若
(
,
,
且
),则
;特别是,当
时,称
为
,
,…
的等差平均项.
(1)已知等差数列
的通项公式为
,根据上述命题,则
,
,
,
的等差平均项为:______ ;
(2)将上述真命题推广到各项为正实数的等比数列中:设
,
,…,
是公比为
的等比数列
中任意
项,若
(
,
,
且
),则______ ;特别是,当
时,称
为
,
,…,
的等比平均项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab14f60ca1a64d70a4dd5a662c6530e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c13c73a017127794debc08dfa029fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de09db4e35fed83c5ac3fb2bbd976906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8976d0f44ad2fa82e9dae988be07f728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b427fbf45913f86cc7b4c3bf1749f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5880f852890d71bb1c95ffe7382e1a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab1031a0c7db08519d6b56729fc7e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0116e1383a146ef6406d514764e87666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de009d9df65374c870a4012cf5db28df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab14f60ca1a64d70a4dd5a662c6530e.png)
(1)已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c211eecfe7c449b52ace8aef55d58.png)
(2)将上述真命题推广到各项为正实数的等比数列中:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab14f60ca1a64d70a4dd5a662c6530e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c13c73a017127794debc08dfa029fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de09db4e35fed83c5ac3fb2bbd976906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8976d0f44ad2fa82e9dae988be07f728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b427fbf45913f86cc7b4c3bf1749f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5880f852890d71bb1c95ffe7382e1a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0116e1383a146ef6406d514764e87666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de009d9df65374c870a4012cf5db28df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab14f60ca1a64d70a4dd5a662c6530e.png)
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8 . 若定义
为
的各位数字之和
,如
,则
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48402431243ccf5e7e01edd64a0b8c3.png)
______ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdcda71db9ead4b03b3671382639f6c5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfab9d144cdaf7dcf5dd7e445fdeca45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabd5c9c1361ad20509b12efe296612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5339b73a9ba1dd11e3e26eb2c60fc521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c4d5735d26bdaa47ea312564862ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48402431243ccf5e7e01edd64a0b8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdcda71db9ead4b03b3671382639f6c5.png)
您最近一年使用:0次
9 . 观察下列等式:
;
;
;
;
;请写出第
个等式______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b559bec1bcdc9829094de953e8c2c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee958096655443badf49a73ff276aa04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d861a90fa655fc914427a502fce6f05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41635108e9c3d76e44420e1cc970bf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516b0acb4d7abaa26ed178418c2343b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ba4e6b48109ec9e10138da17e82aec.png)
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10 . 已知数列
满足
,前n项和
.
(1)求
,
,
的值并猜想
的表达式;
(2)用数学归纳法证明(1)的猜想.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4471e05dc80d3cc7bd8a37cf26a95ecf.png)
(1)求
![](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/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)用数学归纳法证明(1)的猜想.
您最近一年使用:0次