名校
1 . (1)已知k,
,且
,求证:
;
(2)若
,且
,证明:
;
(3)设数列
,
,
,…,
是公差不为0的等差数列,证明:对任意的
,函数
是关于x的一次函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b4b3879d1c6debf0333008f686634e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e10e0bb04d7d261d880aea655e19db1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030d7dbc61a27892cd24b1c4d21745ee.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dbbfed8a6279c3c233cdd1795946ed.png)
您最近一年使用:0次
21-22高一下·上海浦东新·期末
名校
解题方法
2 . 记
是公差不为
的等差数列
的前
项和,已知
,
,数列
满足
,且
.
(1)求
的通项公式;
(2)证明数列
是等比数列,并求
的通项公式;
(3)求证:对于任意正整数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](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/6b106f3aed5e2f23e10c1605045dccbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360d929d12ccfdf847e487cf8eeabf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2669b03c9edf3947bd588e5bb0d800d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9b0e5214575fdbfbe00302189656f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907fce0e59f19c1dfcad75aceac9572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)求证:对于任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8595994167a8784aa79dba19fb4b8e1d.png)
您最近一年使用:0次
解题方法
3 . 如果数列
满足:
且
,则称数列为“
阶万物数列”.
(1)若某“4阶万物数列”
是等比数列,求该数列的各项;
(2)若某“9阶万物数列”
是等差数列,求该数列的通项公式;
(3)若
为“
阶万物数列”,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def85ab2340cabdaf18d4ce634dc2382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a0786747620e2ddecc5358435158d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若某“4阶万物数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若某“9阶万物数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](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/890bac6a077220d5582db2a929b677f9.png)
您最近一年使用:0次
名校
解题方法
4 . 已知数列
为等差数列,且
,
.
(1)求数列
的通项公式;
(2)设
,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/23005bd2386f15812ce36833200d019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0a6acd7996ccc71570b11bd081be48.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7b18da12fab639e07f4ba3fa28a14b.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/08299124b1d23c57a0fb290e0564b34b.png)
您最近一年使用:0次
5 . 已知数列
为递增等差数列,数列
为等比数列,且
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292b6a224fc7539b594c8b73d66f8848.png)
(1)求数列
与
的通项公式:
(2)对任意的正整数
,设
,求数列
的前
项和;
(3)求证
.
![](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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c1da88d583a3ae4818b9ccc3b1242c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c25a09929ddd94b69868d3048a79a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292b6a224fc7539b594c8b73d66f8848.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)对任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230238beeb5b5f30228c16247c63ce24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
(3)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e9dab25cd410e93bf7de3abb619b11.png)
您最近一年使用:0次
解题方法
6 . 在等差数列
中,
,且等差数列
的公差为4.
(1)求
;
(2)若
,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/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0dc13236eaa2bd0cdc0f24beea11fe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac38d4f22fc7608ae65bdec45509ca0.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427569657805270edf0c0150d1f67eb1.png)
您最近一年使用:0次
2024-05-14更新
|
1135次组卷
|
3卷引用:模块五 专题6 全真拔高模拟6(人教B版高二期中研习)
7 . 设数列
为等差数列,前
项和为
.
(1)求数列
的通项公式;
(2)设
的前
项和为
,证明:
.
![](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/1d70f81230f504b54007a05b64b72663.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d6968ee4cf919cea5d9bb309dfadc6.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/99b71dfb5c6c02fa99293d1e365ebc03.png)
您最近一年使用:0次
2024-05-11更新
|
670次组卷
|
3卷引用:浙江省丽水市五校高中发展共同体2023-2024学年高二下学期5月期中考试数学试题
浙江省丽水市五校高中发展共同体2023-2024学年高二下学期5月期中考试数学试题(已下线)专题07 数列通项与数列求和常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题
名校
解题方法
8 . 已知
是各项均为正数的等差数列,其前
项和为
,满足
对任意的
成立.
(1)求
的通项公式;
(2)令
,记
为数列
的前
项和.证明:当
时,
.
![](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/6947966790678dcf4a1c6b9d30f556b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deda945164283569437cda6976fe35ea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d896c0ac826b417ab338050de7c837db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/45deada38f235bf0efb327bc4477034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12993f88db04326b694efa635fc1ef33.png)
您最近一年使用:0次
名校
解题方法
9 . 设数列
的前
项和为
,已知
,
是公差为2的等差数列.
(1)求
的通项公式;
(2)若
,设数列
的前
项和
,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/5ecf69901899bba130968c7a091790d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53955b3deab12fa506241a683ad02d71.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d289d8e284958dbe5e78494e37f3149.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/3f90c342e24dd2af11c6ab820df7a549.png)
您最近一年使用:0次
10 . 设公差不为
的等差数列
的首项为
,且
成等比数列.
(1)求数列
的通项公式;
(2)已知数列
为正项数列,且
,设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc54335d4de8adc7c8d5425ba9ee67f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0e24230de5f84e8937dfbd4fb61450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7c561d49be978dafe36601ba26f536.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/8a790ada33239d9fb562525f819a817d.png)
您最近一年使用:0次
2024-06-13更新
|
1485次组卷
|
2卷引用:四川省成都市树德中学2023-2024学年高二下学期期末数学试题