名校
解题方法
1 . 在无穷数列
中,若对任意的
,都存在
,使得
,则称
为m阶等差数列.在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为m阶等比数列.
(1)若数列
为1阶等比数列,
,
,求
的通项公式及前n项的和;
(2)若数列
为m阶等差数列,求证:
为m阶等比数列;
(3)若数列
既是m阶等差数列,又是
阶等差数列,证明:
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd2c3166d0bfd9e64bdc85081445e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57ae28a9ca230ff60fff6406b06ba96.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/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd2c3166d0bfd9e64bdc85081445e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8483c0e1d0daabfa8130baa9737eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674f03ad5f8c00ce301ecb176fb23277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25fe433dbc540279bc50cf65c7f5fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec50a8616d7700de94ee53c2b5dac43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec50a8616d7700de94ee53c2b5dac43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2024-05-31更新
|
362次组卷
|
3卷引用:贵州省毕节市2024届高三第三次诊断性考试数学试题
2 . 已知数列
满足
,
,
.
(1)求证数列
是等比数列,并求数列
的通项公式;
(2)设
,数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3369ae2337f8d6a049fd8e5a9f313f87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求证数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/017a49f5aebadd0aef6449abb44b8baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a823b63d3f6634f0a294bec20aea0.png)
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3 . 帕德近似(Pade approximation)是法国数学家帕德(Pade)于l9世纪末提出的,其基本思想是将一个给定的函数表示成两个多项式之比的形式,具体是:给定两个正整数m,n,函数
在
处的
帕德近似为
,其中
,
,
,…,
(
为
的导数).已知函数
在
处的
阶帕德近似为
.
(1)求实数a,b的值;
(2)证明:当
时,
;并比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b73a1e9e6afa355710753d576ea991a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8cd76f42911e8c8e57ce761b4541137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52140f46c02b2bde412f89d0977bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85cd03aea30c3ee0093afad048b75c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b63504a4bf0d4861de7909bbc2e4878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd370c3b127fbdb77b6e5c40318328d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1e56c92e2ebdc5d2cae336a01b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e96546b3259afe4add331673fb835c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d307aa65d930bc8e51835eb147de513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d128f7851b7771f95bffbdbf3ced02.png)
(1)求实数a,b的值;
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d0af421900f7a55f52dd805064f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4548db97a06a6f27db6af1dd9b063645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786a32019158f0d2ec126cf189ccf572.png)
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名校
4 . 如图,在四棱锥
中,
,
平面
分别为
的中点,
.
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f089b54ee14e369cf48b528477a64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bf40f6235d0231481c2598e2ba977b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb46aaae98bce8e66848e09c2c1cdbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9801cabc43c024b9c5fac34b7db5d69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5617a404c5a3356753136e5a6b6d51e5.png)
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解题方法
5 . 如图.已知平行六面体
的底面是菱形,
,
.
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4660d993eda4d53b99bbe06a20344462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920a7dec798f1fd44f5830504ab5bdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a0e00113872f921116b6c0c3177d0f.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239198e40085b7dcffbe747c9c265a05.png)
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名校
解题方法
6 . 已知函数
.
(1)若
在定义域内不单调,求a的取值范围;
(2)证明:若
,且
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14dee98f762932a2b717636a20306b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4fb399cd59f3c65462df72b179a628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f967a3906eff362ae1748b5a49f204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed1fdfd6d053610f476731689209d32.png)
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7 . 若数列
和
的项数均为
,则将数列
和
的距离定义为
.
(1)求数列1,3,5,6和数列2,3,10,7的距离;
(2)记A为满足递推关系
的所有数列
的集合,数列
和
为A中的两个元素,且项数均为
.若
,
,数列
和
的距离
,求m的最大值;
(3)记S是所有7项数列
(其中
,
或1)的集合,
,且T中的任何两个元素的距离大于或等于3.求证:T中的元素个数小于或等于16.
![](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/294f5ba74cdf695fc9a8a8e52f421328.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/58eb2bc16ca7ba6db8792eec6e2b48c0.png)
(1)求数列1,3,5,6和数列2,3,10,7的距离;
(2)记A为满足递推关系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23093a3f4c23494a943e3957596fee92.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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2865594c03cd3cfcbf3216cdbf08fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cb4aa359781e637bd2232813fa8a24.png)
(3)记S是所有7项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d7457bc36b80660dc03b668674f065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c458592ba2d5ddd559b8720438a8fe.png)
您最近一年使用:0次
名校
8 . 如图,在三棱柱
中,
,点
在底面ABC的射影为BC的中点,
为
的中点.
平面
.
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de3cc06de62b1310a38ef0cb6450b584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10885aaa1e46c288f82c680857e1eeb.png)
您最近一年使用:0次
2024-05-08更新
|
645次组卷
|
5卷引用:贵州省遵义市2023-2024学年高二下学期5月期中联考数学试题
贵州省遵义市2023-2024学年高二下学期5月期中联考数学试题河南省创新发展联盟2023-2024学年高二下学期4月期中数学试题内蒙古自治区兴安盟2023-2024学年高二下学期学业水平质量检测数学试题(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)
名校
9 . 如图①,在直角梯形
中,
,
,
,E为
的中点,将
沿
折起构成几何体
,如图②.在图②所示的几何体
中:
上找一点F,满足
平面
,求几何体
与几何体
的体积比;
(2)当几何体
的体积最大时,
①求证:
平面
;
②求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47ad7ef0a17747fc54fe058bcb8d1a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6a3413b77478c8d4e1e0389dbf5984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199098479c92e87304b91871172d46e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
(2)当几何体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
②求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c079889aea502b5783046f78728eb1.png)
您最近一年使用:0次
7日内更新
|
415次组卷
|
2卷引用:贵州省贵阳清华中学2023-2024学年高一下学期5月联考数学试题
名校
解题方法
10 . 如图所示,在四棱锥
中,底面
是矩形,侧棱
底面
,
,E是
的中点,过点D作
于点F.求证:
平面
;
(2)
平面
.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d4c42112e0a22f240ce2ae432e5b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df44d1ff1227c4de03ca21ac87f3f86a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1666b45ed176d648dd1764f4a2dbd73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
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