1 . 已知数列
.
(1)求
为等比数列,并求
的通项;
(2)令
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c645f7064bb9ebb1e43b5fa2ec733e3e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4f0d92b96d898e84c3367e5ef02140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd8bbf27542757653a403d517871700.png)
您最近一年使用:0次
解题方法
2 . 已知实数列{
},
|满足
.数列{
}是公差为p的等差数列,数列
是公比为p的等比数列.
(1)若
,求数列{
}的通项公式;
(2)记数列
,
的前n项和分别为
,
.若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1ecb4496261accb7611f75e9bb9037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215c0a9a273de67b95fbbe22dcd90b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2da88be606b116c847d0e3b7ba93a1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea49f8a2b98b542b1ebb2ac813346c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f42e60dcbccbdbab9643d323b4398f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5d95a2662414bf57b1449ff7a3ea27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bd7994cf5e961f9cefe77b7ef6737a1.png)
您最近一年使用:0次
3 . 已知数列
是以
为首项,
为公比的等比数列,数列
满足:
,
,
.
(1)求数列
的通项公式;
(2)(i)若
,记
,求数列
的前
项和
;
(ii)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66bb6e83ad3cbc442497efd7e2022955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f99489791db717b082bd96abb88c55e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25a43750117688497649756db5f314d0.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)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442975827582bb10187b047d30109940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c2f7b6c69594d398be19bce9075995.png)
您最近一年使用:0次
20-21高二下·浙江·期末
解题方法
4 . 设等差数列
的公差为d,d为整数,前n项和为
,等比数列
的公比为q,已知
.
(1)求数列
与
的通项公式;
(2)求数列
的前n项和为
;
(3)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babd3af8d92d9af9d1560606f71e064b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda289a8fdf0b1bc96bcca6b878764c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f95ce9d509a67c963d8b6d8c33e04b.png)
您最近一年使用:0次
5 . 数列
中,
,
.
(1)求证:存在
的一次函数
,使得
成公比为2的等比数列;
(2)求
的通项公式;
(3)令
,求证:
.
![](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/de9270716cb03e4277232f75272790de.png)
(1)求证:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9b45b61ad94b1cd444bbc5e52b545e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb381fb2e31d337bd434fdb455f5acb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113b99818fd5706165bb9f52aab06eb0.png)
您最近一年使用:0次
6 . 已知数列{an},{bn},{cn}中,
.
(Ⅰ)若数列{bn}为等比数列,且公比
,且
,求q与{an}的通项公式;
(Ⅱ)若数列{bn}为等差数列,且公差
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9206d70a66fa292da14da37b07dfb7.png)
(Ⅰ)若数列{bn}为等比数列,且公比
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71acdb04454c77e1e25ad4f336cccfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619a9ccf06d7a200fd5735268604b095.png)
(Ⅱ)若数列{bn}为等差数列,且公差
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e17130fa015847640e22f88bb4087d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d307ec71820b6536453fbdb5069da3.png)
您最近一年使用:0次
2020-07-09更新
|
14527次组卷
|
70卷引用:2020年浙江省高考数学试卷
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7 . 已知数列
满足
,
,
,
,且
是等比数列.
(1)求数列
的通项公式;
(2)①求证:
为等比数列;
②记
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ecf69901899bba130968c7a091790d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bbb67593c95bab93ff67145ae95ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b30350893f0daaad2e1b5e33e5d42fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76246142f42140b47b199684ac7d1a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5631660fefbdbf89c6bebada4f92f1cf.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae099412ea80b214352e048c989271ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
8 . 已知
为公差不为
的等差数列,
是等比数列
的前
项和,若
是
和
的等比中项,
,
.
(1)求
及
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb88d8831173a3319d95c502110ab31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c340fdadffa2f9120a70430ce477f8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e30678cd4f299ef67b719f13bfa863a.png)
您最近一年使用:0次
9 . 已知数列
满足
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e726e6d2a39e7df97937817391ac309.png)
,且
是等比数列.
(1)求数列
的通项公式;
(2)①求证:
为等比数列;
②求证:对于任意
,都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ecf69901899bba130968c7a091790d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bbb67593c95bab93ff67145ae95ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b30350893f0daaad2e1b5e33e5d42fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e726e6d2a39e7df97937817391ac309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bc2b05dc79b18ecb4ac3f9b5c492d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5631660fefbdbf89c6bebada4f92f1cf.png)
②求证:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cff7b659a58e3a9f106feabb612cd4.png)
您最近一年使用:0次
名校
解题方法
10 . 数列
是等比数列,公比大于
,前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
,
是等差数列,已知
,
,
,
.
(1)求数列
的通项公式
,
;
(2)设
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
,
(ⅰ)求
;
(ⅱ)若
,证明
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.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/28d82e4c2294efbd33e1b268e9a0cec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b840f977d70d2c0393528b91661c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb0ae3ee83a722a6ea7774db46661c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d462a9d1eeb119638c72761db74d1690.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.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/28d82e4c2294efbd33e1b268e9a0cec5.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2711fcd2e88272be88e0423eec96928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297e437499bcb77a9c5ae6400d6e47cb.png)
您最近一年使用:0次
2020-03-19更新
|
1286次组卷
|
5卷引用:2019届浙江省杭州市学军中学高三下学期5月模拟考试数学试题