10-11高一下·广东惠州·期末
1 . 设
为数列
的前
项和,对任意的
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ab8b33ce55c7272369453d2ed5212b.png)
为常数,且
.
(1)求证:数列
是等比数列;
(2)设数列
的公比
,数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9938322554d76ce76016bdee547f85.png)
,
),求数列
的通项公式;
(3)在满足(2)的条件下,求证:数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ab8b33ce55c7272369453d2ed5212b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de562860972bdb1f46843689a14ae69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f06dee2b6ccd65644064249183787e.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da10fd196174f5e4b3bace35bc81d9a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9938322554d76ce76016bdee547f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d6d999382aec4acb0ca4e87cc92955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)在满足(2)的条件下,求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478d46f61ea4758a07c1a899925937ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d1c1af9a4bb88df8dfc79c5fa064a9.png)
您最近一年使用:0次
10-11高一下·黑龙江·期中
解题方法
2 . 已知数列
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07cf03f2a95f48212e922c4f0a6b6caa.png)
(1)设
,求数列
的通项公式;
(2)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07cf03f2a95f48212e922c4f0a6b6caa.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c7eb0282d89c5dfa3a23a278ded2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
您最近一年使用:0次
10-11高一下·吉林长春·期中
3 . 已知数列
中,
,
,
.
(1)求数列
的通项公式;
(2)设
,求数列
的前n项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f32547fddc2c62ad15ba5c10ef68df1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
10-11高一下·黑龙江牡丹江·期中
4 . 已知数列
满足
.
(1)求
;
(2)求数列
的通项公式;
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4515daf25c559a05c82c36b3c0950a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2ff81d91e7a8edd2719c8e3e09751e.png)
您最近一年使用:0次
10-11高一下·安徽合肥·期中
5 . 已知数列
满足
.
(1)求证:数列
是等比数列;
(2)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a423748aafcc4f2e66381bd528f7e33.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
10-11高一·湖北黄冈·期中
6 . 已知
为数列
的前
项和,且
,
,
(Ⅰ)求证:数列
为等比数列;
(Ⅱ)设
,求数列
的前
项和
;
(Ⅲ)设
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/31796a8541a408f66f925b370fcb5648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bce6187f3f11e0ceead8a645f5f9d32.png)
(Ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd08dea792140965eccea3442635d328.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e96034624bc8722caa564d2cd1e6b1.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/bf83e20035c3afd6d26ebfd53d768a70.png)
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1207d2d76e3a37ee00b281771b95e064.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52f9758f38f20362b2d27133a9d436d.png)
您最近一年使用:0次
真题
名校
7 . 已知数列
的首项
,其前
项的和为
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c26b75756a6fd2a865a557df21d9b7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56edc58f076524e70d62c9ff98d64919.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/19099d49dd72256696a7e7f8013eaae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c26b75756a6fd2a865a557df21d9b7e.png)
A.0 | B.![]() | C.1 | D.2 |
您最近一年使用:0次
2016-11-30更新
|
149次组卷
|
2卷引用:上海市第三女子中学2018-2019学年高二上学期期中数学试题
2010·北京海淀·二模
名校
8 . 已知数列
满足
,
(
N
),则
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98fd571f61de05068600bcd487db625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b0aafc603ba02b6702e785b00a5013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec53fd82557a22187381f646a5b8293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bad650c3afe662a5be4a82cd533356f.png)
您最近一年使用:0次
9-10高二下·河南郑州·期中
解题方法
9 . 已知数列
满足
,
,设
.
(1)求
;
(2)证明:数列
为等比数列;
(3)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a325593b8ef98ff901e6a37b57552e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cefac60bb3fcde0bded804501c90b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
9-10高三·福建宁德·阶段练习
10 . 已知正项数列
中,
,点
在函数
的图像上,数列
中,点
在直线
上,其中
是数列
的前项和,
.
(1) 求数列
的通项公式;
(2) 求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0391da6e1057ac401356adfab040e182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc53bf2976eca3ef7b18950d04591fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb3dbdb1a256f18eb8e1673598583c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29429f8289a3128bc9cf3823fb068042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633d50992e41628a9f5ce362f45f2a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b03db60f1a6f0beb5de21991bd19cf.png)
(1) 求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
(2) 求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次