1 . 已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
是否是等比数列?若是,给出证明;否则,请说明理由;
(2)若数列
的前10项和为361,记
,数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04053ecf80b3bb9179c8baab47bf8dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc0cf1f0a00718b95a2a4fffd11dd32.png)
您最近一年使用:0次
2023-08-20更新
|
2550次组卷
|
9卷引用:安徽省池州市第一中学2024届高三上学期“七省联考” 数学模拟练习(2)
2 . 已知数列
满足
,
,
,
.
(Ⅰ)求证:数列
为等差数列;
(Ⅱ)设数列
的前
项和
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42162d21f041e1fa9df1f583d80a2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
(Ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0cab513667aaae70e590ba73efff7dc.png)
(Ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b2286a94a516e6a2fb45329a772fd4.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/e8695875aded32578fcc9a86177b1ea6.png)
您最近一年使用:0次
2021-05-12更新
|
797次组卷
|
4卷引用:安徽省安庆市2021届高三下学期二模理科数学试题
名校
解题方法
3 . 已知数列
满足
,
(
,
),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
(1)证明数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
为等比数列,求出
的通项公式;
(2)数列
的前项和为
,求证:对任意
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2438f2272d7b7ab51dbbe587025a553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd675707e7b2a293d35c2c2690c13c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d307ec71820b6536453fbdb5069da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3860c78a8d25ac6b5c1cff5ebbd960fc.png)
您最近一年使用:0次
2020-11-07更新
|
1083次组卷
|
9卷引用:【市级联考】安徽省合肥市2019届高三下学期四月临考冲刺卷数学(理)试题
【市级联考】安徽省合肥市2019届高三下学期四月临考冲刺卷数学(理)试题【全国百强校】河北省唐山市第一中学2019届高三下学期冲刺(一)数学(理)试题湖北省襄阳五中、夷陵中学、钟祥一中三校2020届高三下学期6月高考适应性考试理科数学试题宁夏银川一中2021届高三第三次月考数学(文)试题宁夏银川一中2021届高三第三次月考数学(理)试题湖北省荆州中学2020-2021学年高二上学期12月月考数学试题四川省南充市白塔中学2020-2021学年高一下学期第二次月考(6月)数学试题河南省周口市太康县第一高级中学2022-2023学年高二上学期第一次月考数学(文科)试题 河南省周口市太康县第一高级中学2022-2023学年高二上学期第一次月考数学(理科)试题
2010·湖南长沙·一模
4 . 已知
.
(1)若
,函数
在其定义域内是增函数,求
的取值范围;
(2)当
,
时,证明:函数
只有一个零点;
(3)若
的图像与
轴交于
,
两点,
中点为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a6999eea23ebccc533ed84fb3a97b4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec3d75e53b990bc8f9a4622928dd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ae7486a9ecc9fa47de8b07cbee9677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af086f84a7f1160bfdece867dbfa0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9ba87bd7d301f0c861ce0985b7e299.png)
您最近一年使用:0次
2016-11-30更新
|
613次组卷
|
4卷引用:【全国百强校】安徽亳州市涡阳一中2018届高三最后一卷数学理试题
【全国百强校】安徽亳州市涡阳一中2018届高三最后一卷数学理试题(已下线)湖南省长沙市一中2010届高三第一次模拟考试文科数学试题(已下线)湖南省长沙市一中2011届高三年级月考(一)数学试题(理科)2019届百师联盟全国高三冲刺考(四)全国 II 卷数学(文)试题
名校
5 . 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)
您最近一年使用:0次
2016-12-04更新
|
1595次组卷
|
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
6 . 如图,在四面体
中,
,
,
两两垂直,
,
是线段
的中点,
是线段
的中点,点
在线段
上,且
.
平面
;
(2)若点
在平面
内,且
平面
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0f630195bcf6c3ca8f4fdeff43b082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e3c9755dbd39fb01de614840d230f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cf187bc2ede965870b90757b495f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c5ef850e256c98ca4f033999e61311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c015d99f2677951bdcd0447240ef93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
名校
7 . 如图,在三棱台
中,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/13/c8d56a2f-4382-453b-ade3-645ecbaf736b.png?resizew=161)
(1)求证:
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744c13d7a552602487e83ad827cf8e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/13/c8d56a2f-4382-453b-ade3-645ecbaf736b.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7852669d7f32cdad2880e22aaf1d5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
您最近一年使用:0次
2024-06-12更新
|
650次组卷
|
3卷引用:安徽省安庆市第一中学2024届高三下学期6月第四次模拟(热身考试)数学试卷
名校
8 . 如图,在三棱台
中,
,平面
平面
,
.
平面
;
(2)若三棱锥
的体积为
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1638b1b615ff368c456cc1fbbcd0464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50eda31bbc3d40f0b305d4ac673fc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2024-05-13更新
|
888次组卷
|
4卷引用:安徽省合肥市一六八中学2024届高三下学期最后一练数学试题
名校
9 . 如图,四棱锥
中,四边形
是菱形,
,
是正三角形,
是
的重心,点
满足
.
平面
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566a4158b0fb4670a68c61cf12c1bad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a779876cdfb2c489ad0eaed0f73e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38711ce72877e0c4b4523f6f9b5a2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
您最近一年使用:0次
名校
10 . 学校食堂为了减少排队时间,从开学第
天起,每餐只推出即点即取的米饭套餐和面食套餐.某同学每天中午都会在食堂提供的两种套餐中选择一种套餐,若他前
天选择了米饭套餐,则第
天选择米饭套餐的概率为
;若他前
天选择了面食套餐,则第
天选择米饭套餐的概率为
.已知他开学第
天中午选择米饭套餐的概率为
.
(1)求该同学开学第
天中午选择米饭套餐的概率;
(2)记该同学开学第
天中午选择米饭套餐的概率为
证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
(1)求该同学开学第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)记该同学开学第
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4卷引用:安徽省黄山市2024届高中毕业班第二次质量检测数学试题
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