名校
1 . 已知无穷数列
中,
是以10为首项,以-2为公差的等差数列;
是以
为首项,以
为公比的等比数列
;并且对一切正整数
,都有
成立
(1)当
时,请依次写出数列
的前12项;
(2)当
时,求
的值;
(3)设数列
的前
项和为
,问是否存在
的值,使得
成立?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4811e3603e8790c25aaf91c41d7c7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c7c1d3e2e2eeceb2edf3c4d1d78452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3677fad234da0d284ba3ecc710c9a62e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c453d55bd2873e4469273132c421e7b3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb15a25b2e913e233d8ee87d4cb78b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设数列
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1640b1e0848ae4e0d681e4e5e4589652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
2 . 给定一个n项的实数数列
,任意选取一个实数c,变换
将数列
变换为数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5280b3866264f8c266fbcfc3de96fe.png)
,再将得到的数列继续施行这样的变换,这样的变换可以连续施行多次,并且每次所选择的实数c可以不相同,将第
次变换记为
,其中
为第
次变换时选择的实数.如果通过k次变换后,数列中的各项均为0,则称
为“
次归零变换”,如
项数列
有“
次归零变换”
.
(1)对数列
,请给出其一个“
次归零变换”,其中
;
(2)求证:对任意
项数列,都存在“
次归零变换”;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53032c9a9a3edca24a7ed909e29a58b.png)
(3)分别判断两个数列
与![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b09a30c1f614670c58260ac05637fa6.png)
是否存在“
次归零变换”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71440f7f7adb82343de4e1fe714844c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e5927e6b179a7df32697f18ba04b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5280b3866264f8c266fbcfc3de96fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd261890430da46de995859443c31a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0c165709cb397edbdf03aecee92bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5925987d5a6eb1ce1fec68b810cb6fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb41001678e62a7f251aca18ba87223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392131fb1129db593075a41e42614c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1925f666f670a98809ce07b2db292642.png)
(1)对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63541441d26f277d9ed7816c089c6b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32122984badd2651714490544ab42682.png)
(2)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc321599521a98661ed719cc82ca87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53032c9a9a3edca24a7ed909e29a58b.png)
(3)分别判断两个数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f28c61ca6fda7a77fdae8b39b41519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b09a30c1f614670c58260ac05637fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4259bd8918d091c52eb0bd5e3e0805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3493454f81c555d65d46357d719c5fdf.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,无穷数列
满足
,
.
(1)若
,写出数列
的通项公式(不必证明);
(2)若
,且
,
,
成等比数列,求
的值;问
是否为等比数列,并说明理由;
(3)证明:
,
,
,
,
成等差数列的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ae4c96befd0583a42ba46a7470a49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6aa8089b5d9b722aff679af3c4d289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)证明:
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
您最近一年使用:0次
2021-12-20更新
|
423次组卷
|
2卷引用:上海财经大学附属北郊高级中学2023届高三上学期开学考试数学试题
解题方法
4 . 已知无穷数列
与无穷数列
满足下列条件:①
;②
.记数列
的前
项积为
.
(1)若
,求
;
(2)是否存在
,使得
成等差数列?若存在,请写出一组
;若不存在,请说明理由;
(3)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66ba9376feb1cb58b80abd17ab638a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9487a417f7059568539f6f39cce57681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92cf3be68720dfac5c5ebfbdb7e782c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2114a0fe21dc0e5bf831c146ef02b113.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a447e5baee4f7518706498d4aca7553b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3577ef49a3177a78392e720ea4a04.png)
您最近一年使用:0次
2021-05-05更新
|
757次组卷
|
5卷引用:上海市奉贤区致远高级中学2022届高三下学期开学评估数学试题
上海市奉贤区致远高级中学2022届高三下学期开学评估数学试题上海市杨浦区2021届高三二模数学试题(已下线)课时22 数列、等差数列、等比数列-2022年高考数学一轮复习小题多维练(上海专用)(已下线)考向16 数列求和及数列的综合应用-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)考向21数列综合运用(重点) - 2
5 . 已知正整数数列
满足:
,
,
.
(1)已知
,
,求
和
的值;
(2)若
,求证
;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55ef34345210312db273ab4981c40f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf89aa413e6db9a800fae7798718108e.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f86a8746a583f411fb73c6334eb27b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2367e607a23ebf82ed2b859aadd57952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efac4bb9d79292964399cb51379c6657.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
2021-03-22更新
|
1040次组卷
|
4卷引用:上海市建平中学2021届高三下学期开学考试数学试题
上海市建平中学2021届高三下学期开学考试数学试题(已下线)考向18 数列不等式-备战2022年高考数学一轮复习考点微专题(上海专用)浙江省2021届高三4月份高考数学模拟试题(10)(已下线)模块九 数列-2
6 . 我们称满足:
(
)的数列为“
级梦数列”.
(1)若
是“1级梦数列”且
,求
和
的值;
(2)若
是“1级梦数列”且满足
,
,求
的最小值;
(3)若
是“0级梦数列”且
,设数列
的前
项和为
,证明:
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2fa3ec054db237c3dc3f6785253eeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d116ca533beba0630be998d6ff1214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930de0d297e940bbf1faab22ff70b8b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79c9c1e08cdce10e202984d1a228c27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc22e7024a7dc8f5e6f7869bf1e41c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42bd0954c485ed2b67cfd38f1acf6c75.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199501da83fb2f3062167a17565c17bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea49f8a2b98b542b1ebb2ac813346c90.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/46514294c73c544d81505d82ecd5a22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.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
、
、
成等差数列,求
的值;
(2)若
,求数列
的通项
;
(3)若对任意正整数
,都有
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a3def0fd2ff496d99c13c6f933d404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)若对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76ca08fb2d8577f0b0e5b16e5c98693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2019-11-11更新
|
463次组卷
|
2卷引用:上海市敬业中学2022届高三下学期开学考试数学试题
名校
8 . 设数列
的前n项和为
,对一切
,点
都在函数
的图像上.
(1)证明:当
时,
;
(2)求数列
的通项公式;
(3)设
为数列
的前n项的积,若不等式
对一切
成立,求实数a的取值范围.
![](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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e6e0e0522300b27c59ea1920a7b725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc15b8864ee2c70e75b70684b7a2b5e.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c7aab4df25884973273efae244f2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed7ec1c3d7cd0cb093d0f961e0cc98ed.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09953c3d3c8bb8566bb740c3a7d53e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b61d7a09e11d3bfa0386402e9de9e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
您最近一年使用:0次
2019-11-04更新
|
905次组卷
|
5卷引用:上海市曹杨二中2016-2017学年高二上学期开学摸底考试数学试题
上海市曹杨二中2016-2017学年高二上学期开学摸底考试数学试题上海市曹杨二中2019-2020学年高二上学期10月月考数学试题上海市七宝中学2017-2018学年高二上学期10月月考数学试题(已下线)必刷卷02-2020年高考数学必刷试卷(新高考)【学科网名师堂】-《2020年新高考政策解读与配套资源》(已下线)卷02-2020年高考数学冲刺逆袭必备卷(山东、海南专用)【学科网名师堂】
名校
9 . 将边长分别为
的正方形叠放在一起,形成如图所示的图形,由小到大,依次记各阴影部分所在的图形为第1个、第2个、……、第
个阴影部分图形.设前
个阴影部分图形的面积的平均值为
.记数列
满足:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/85fe9e1f-d2b7-480e-8c1e-f4970f28d4bf.png?resizew=204)
(1)求
的表达式及数列
的通项公式;
(2)记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f159b459dbd5a85c476a928872087167.png)
若
,其中
为常数,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c47641a6b8b89bc3553f6422ed8b75.png)
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5f42bc87ce3ff0d8d85676cf3c61b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a1da2bc7852fca74e47e3454d4a9fc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/85fe9e1f-d2b7-480e-8c1e-f4970f28d4bf.png?resizew=204)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f159b459dbd5a85c476a928872087167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a7cd39c1bfc679d4a9373a47ebaeba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92bb35fc7fbb1729102c816f12b1b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c47641a6b8b89bc3553f6422ed8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb889bf1d1cee795569693d9552be711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
您最近一年使用:0次