1 . 在数列
中,已知
.
(1)证明数列
是等比数列,并求数列
的通项公式;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c9c623982f68603b971b20f97ed606.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e06816992e1b854b5d4dae9a957b5e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd613cd582d671b532eb774f44233ea.png)
您最近一年使用:0次
名校
2 . 已知数列
前
项和为
,满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e375b8b3791ee98dab11cd97b6379f.png)
(1)证明:数列
是等差数列,并求
;
(2)设
,求证:
.
![](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/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e375b8b3791ee98dab11cd97b6379f.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f543f3aafa4740bd65aefc8d8de4b6f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ac75838b14085b34c59a0eb385ac4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b340e6cfa6ab9b97da7409f2db62c00.png)
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2016-12-03更新
|
865次组卷
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5卷引用:安徽省六安市第一中学2018-2019学年高一下学期期末数学试题
2014·广东揭阳·一模
名校
3 . 如图,四棱锥
的底面是正方形,侧棱
底面
,过
作
垂直
交
于
点,作
垂直
交
于
点,平面
交
于
点,点
为
上一动点,且
,
.
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571662604017664/1571662609547264/STEM/d37a330f8ff643178e2a1b9fd39f4a81.png?resizew=115)
(1)试证明不论点
在何位置,都有
;
(2)求
的最小值;
(3)设平面
与平面
的交线为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72406478fda1c6e3b8052467385a3bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1804c3641953c30ccf750504eff6577.png)
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571662604017664/1571662609547264/STEM/d37a330f8ff643178e2a1b9fd39f4a81.png?resizew=115)
(1)试证明不论点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268559207a04b28fe35a1198bda23019.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ef145010ce1a0c3119392e75e64548.png)
(3)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6880c154f373d04de8976d123a9ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9835a52bc3f085d5e1a5a3b331037cc.png)
您最近一年使用:0次
2013·江苏·一模
名校
4 . 在平面直角坐标系xOy中,如图,已知椭圆C:
+
=1的上、下顶点分别为A、B,点P在椭圆C上且异于点A、B,直线AP、PB与直线l:y=-2分别交于点M、N.
![](https://img.xkw.com/dksih/QBM/2013/4/11/1571182578401280/1571182583971840/STEM/62ce629f-5beb-44da-ae7e-70a6d6b344ed.png)
(1)设直线AP、PB的斜率分别为k1,k2,求证:k1·k2为定值;
(2)求线段MN长的最小值;
(3)当点P运动时,以MN为直径的圆是否经过某定点?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de95471bb6c16acb4fd84d8315e6a637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a476588acbf41d798cc234a52fa21a8.png)
![](https://img.xkw.com/dksih/QBM/2013/4/11/1571182578401280/1571182583971840/STEM/62ce629f-5beb-44da-ae7e-70a6d6b344ed.png)
(1)设直线AP、PB的斜率分别为k1,k2,求证:k1·k2为定值;
(2)求线段MN长的最小值;
(3)当点P运动时,以MN为直径的圆是否经过某定点?请证明你的结论.
您最近一年使用:0次
2016-12-02更新
|
1047次组卷
|
5卷引用:安徽省安庆市九一六学校2020-2021学年高二下学期开学考试数学(理)试题
安徽省安庆市九一六学校2020-2021学年高二下学期开学考试数学(理)试题(已下线)2013届江苏南师附中、天一中学等五校高三下学期期初教学质量调研数学卷(已下线)2014届江苏省扬州中学高三开学检测文科数学试卷(已下线)2013届江苏南师附中高三下学期期初教学质量调研数学试卷上海市金山中学2016-2017学年高二下学期3月段考数学试题
5 . 如图,在梯形
中,
,平面
平面
,四边形
是矩形,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/2016/10/26/1573096458485760/1573096464900096/STEM/2e5ea30e941c439bbb944473a83f0b7b.png?resizew=220)
(1)求证:
平面
;
(2)当
为何值时,
平面
?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86dcc8ff4b695ec09f0e352e6a7810d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0db1f4f666a9be9ede868065a50997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2016/10/26/1573096458485760/1573096464900096/STEM/2e5ea30e941c439bbb944473a83f0b7b.png?resizew=220)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
您最近一年使用:0次
2016-12-04更新
|
1511次组卷
|
3卷引用:安徽省“皖南五十校”2016-2017学年高一下学期末联考数学试题
6 . (1)已知
,证明:
;
(2)求证:函数
在
上为减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d83da45ca0235310ff073fe43186ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6559c2b7c9625ac714bf69b00476c5.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad66314a685ceb505532373a3a4acc08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92fa19367789433056aacc9496312c34.png)
您最近一年使用:0次
名校
解题方法
7 . 已知数列
,
,其前
项和
满足
,其中
.
(1)设
,证明:数列
是等差数列;
(2)设
,
为数列
的前
项和,求证:
;
(3)设
(
为非零整数,
),试确定
的值,使得对任意
,都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.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/851afb5fa82c3e4448ac7b674d143cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fdb807b6968c2986392b64b4fca2d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819480e1e624208f729ad8653e4f24f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18230ed18623e12c2d46d055cb16df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4a37ac219023581db07fe5961ae460.png)
您最近一年使用:0次
2016-12-03更新
|
1277次组卷
|
4卷引用:2016-2017学年安徽六安一中高二文上段测二数学试卷
11-12高二上·浙江金华·阶段练习
名校
8 . 若直线l:x+my+c=0与抛物线y2=2x交于A、B两点,O点是坐标原点.
(1)当m=﹣1,c=﹣2时,求证:OA⊥OB;
(2)若OA⊥OB,求证:直线l恒过定点;并求出这个定点坐标.
(3)当OA⊥OB时,试问△OAB的外接圆与抛物线的准线位置关系如何?证明你的结论.
(1)当m=﹣1,c=﹣2时,求证:OA⊥OB;
(2)若OA⊥OB,求证:直线l恒过定点;并求出这个定点坐标.
(3)当OA⊥OB时,试问△OAB的外接圆与抛物线的准线位置关系如何?证明你的结论.
您最近一年使用:0次
2016-12-01更新
|
856次组卷
|
4卷引用:安徽省池州市东至县第二中学2020-2021学年高二下学期3月月考文科数学试题
安徽省池州市东至县第二中学2020-2021学年高二下学期3月月考文科数学试题(已下线)2011-2012学年浙江省东阳中学高二12月阶段性检测理科数学试卷(已下线)2011-2012学年山东省汶上一中高二12月月考理科数学辽宁省锦州市联合校2021-2022学年高二上学期期末模拟数学试题(锦州五高命题)
名校
9 . 已知数列
中,
,
.
(1)证明数列
为等比数列,并求
的通项公式;
(2)数列
满足
,数列
的前
项和为
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381576e698a46df8c497e6b5f8346ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac0ecbbd0b66ccaa554cf4eb1a8bace.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ef3b81f7bcaf96d4f19f3e36fc4683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2448cf72af76b810310e4cfb9818e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad1bb0c3413becc1ed1d944d4521096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2448cf72af76b810310e4cfb9818e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb26cd1601fe7e76e1e2dc0b4909324a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eebcedd49ea382753d28893391ee7a59.png)
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2016-12-04更新
|
1595次组卷
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7卷引用:【全国百强校】安徽省安庆市第一中学2018届高三热身考试数学(文)试题
10 . 如图,四棱锥
中,四边形
是正方形,若
分别是线段
的中点.
![](https://img.xkw.com/dksih/QBM/2015/11/18/1572294899572736/1572294905634816/STEM/8ea5fb7dff814c378a660541c3584e17.png)
(1)求证:
||底面
;
(2)若点
为线段
的中点,平面
与平面
有怎样的位置关系?并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c02fd797129dd2d7936d7fdedee3ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a003de8409231a347edebc8284be186c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85de410d85be189dfa5aabb33410b896.png)
![](https://img.xkw.com/dksih/QBM/2015/11/18/1572294899572736/1572294905634816/STEM/8ea5fb7dff814c378a660541c3584e17.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2015/11/18/1572294899572736/1572294905634816/STEM/c2cdc41effea432ba40eddc294d8a1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2016-12-03更新
|
1048次组卷
|
5卷引用:安徽省滁州市定远县育才学校2020-2021学年高二上学期第二次月考数学(文)试题