1 . 已知各项均为正数的数列
的前n项和为
,
,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edeb68b363f9771e9bc4d01a6cc7725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4e70b360f988fdbd92300ab22c4613.png)
A.511 | B.61 | C.41 | D.9 |
您最近一年使用:0次
2 . 已知数列
是正项等比数列,
是等差数列,且
,
(1)求数列
和
的通项公式;
(2)
,求数列
的前
项和.
(3)
表示不超过
的最大整数,
表示数列
的前
项和,集合
共有4个元素,求
范围;
![](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/51d1eecd0ba6347401e36612efcf0005.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adeec5eaea5f88f69d96dd0c54ccd305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ef48976a52cc4a2be7c46a98426c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba903eeaf0719775fe0de71949f643f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b17a9b9bb8bf6bb9865e37f204da5c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4b73c9f0ec3ad00e5a535e7678185b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
3 . 已知数列
是等差数列,
,
,数列
的前n项和为
,且
,
(1)求数列
和
的通项公式;
(2)若集合
中恰有四个元素,求实数
的取值范围;
(3)设数列
满足
,
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b61bd1c49c3310b78a3127ee668ec145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8d5ef4302d8b46b28dda938d22500e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e3a9bb248d5c1580b04a35bf884100.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b04a22b696271b8d4597d48a9838f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145277adb96fc94f05367b50094b07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f85c8d9210c7328fbe3d653ffede057.png)
您最近一年使用:0次
4 . 设
是等差数列,其前
项和
,
是等比数列,且
,
,
.
(1)求
与
的通项公式;
(2)设
,求数列
的前
项和
;
(3)若对于任意的
不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85444874c705666de9488286d3d61dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1273751a0b5a984cf01c2d0e00e474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9651204c54475c2e8cda8d0a6eeba177.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca3f045d6f1fbdf6feedaf05363575b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2771c5f04582c545e0f9afc8a2cb9597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161ac25d7a41e3e2b5bbb4166153ad4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
5 . 已知
是等差数列,
是公比为正数的等比数列,且
,
,
,
.
(1)求数列{
,
的通项公式;
(2)设
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2d56dd30fff703753578f20d797a97.png)
(ⅰ)求
;
(ⅱ)求
.
![](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/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55c6c2303f63c7ca868120cddf11643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6822ba1b661cddc1d744e23c4f9503f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355f362a3cdd8067cf5a70307f1af2d9.png)
(1)求数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc852a14e0404b9345742f42551eab09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2d56dd30fff703753578f20d797a97.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba67146c41dba11b545dcb79e6ebfec.png)
您最近一年使用:0次
6 . 已知
是等差数列,
,
,数列
的前
项和为
,且
,
(
).
(1)求
和
的通项公式;
(2)求
;
(3)设数列
满足
(
),证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815496d28bd104caf952d6f2cf2b9696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917b229d7588aa46a4f1a724132d1c07.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/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5775bfc74af2d9702dabfcf88337a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85d54cde25c21818ce96435987fb5a4.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a2ad745e523e3c33b21746cc02ea4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0da8551dff1064f03b775ef82909207.png)
您最近一年使用:0次
名校
解题方法
7 . 已知数列
满足
,其中
.
(1)若
,求数列
的前n项的和;
(2)若
,
且数列
满足:
,证明:
.
(3)当
,
时,令
,判断对任意
,
,
是否为正整数,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2409b15bd3f95696d9ee5255b04d0313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c3287bc9d86ab480f718609672d6e0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2385f5c338bb07f5aa51c85c39e412e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94436c52b50b0f9e0bf51ea543bcfe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ed618688b3113849ea49b9df7082ef.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535fd9605b90ac7f0fed6025be9f851f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf77ab807b5b3d8d6e8c52315adf92a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
解题方法
8 . 已知
为数列
的前n项和,且满足
,其中
,且
.
(1)求数列
的通项公式;
(2)设
,若对任意的
,都有
,求实数m的取值范围.
![](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/20ad78a8406ccbc39757d76de8bd3a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9810a2aa6e858b26e47fd989c7c894d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790fd1b4fe3a98055b08bcb9d332f072.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6bf08cb90a5348df08b47927572a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b38c5eaa8d94e0dc1c48c36e7649945.png)
您最近一年使用:0次
9 . 记
是等差数列
的前
项和,数列
是等比数列,且满足
,
.
(1)求数列
和
的通项公式;
(2)设数列
满足
,
(ⅰ)求
的前
项的和
;
(ⅱ)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67616cc8020d5749ff70aa860933a90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e11d8be3e39431d9fcba33aa04877faa.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f8c71fc5228f7679e5ef8f9aae1630.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2def5aa62f497709e1bd8258583d62fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35926bf4b8e2c163c20942173cffcce.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b6ba3b9f5a95c2c8fe6d0dce686e67.png)
您最近一年使用:0次
10 . 已知数列
是等比数列,
,
,
,
成等差数列.
(1)求
的通项公式和
;
(2)数列
满足
;当
时,
;当
时,
.记数列
的前
项和为
.
①若
,求
的值;
②若
,求证:
.
![](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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d473bfcc52ebc119430335531488a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8822db269777fddd605b50521576b57.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5adec817865eefb615fb692c4b7f473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f536ba19aa3c3b1be97b33dfd852f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f205eb08ae9ffe22dc6fbfe2b1fe65fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b434cd915f3e6fbc3028f86f358332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3054785bacfe0537831c337f57ab92.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)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b54a7884388655cea734328f3e43f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59268f6dd353af2dedd8269a2bc5b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0f924858fdfc9403142fcbce46de32.png)
您最近一年使用:0次