解题方法
1 . 已知抛物线
:
,直线
与抛物线
交于
,
两点,
为坐标原点.
(1)若直线
过
的焦点
.
(
,
)与
交于四点
,
,
,
,记弦
,
的中点分别为
,
,求证:线段
被定点平分,并求定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(i)当的面积最小时,求直线
的方程;
(ii)当,记
的外接圆
与
的另一个交点为
,求
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a01cad957bd5a9e4f0c931cf5510a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
名校
解题方法
2 . 数列
满足
则称数列
为下凸数列.
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
,其中
,
分别是公比为
,
的两个正项等比数列,且
,证明:
是下凸数列且不是等比数列;
(3)若正项下凸数列的前
项和为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0bee75d4d83c0b76421fd87113e4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f67fc95a626251da11649acb5e1706f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c340d7d093dd4a275ffea4b87cd26827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171ff5c2728e7cf00a88f88de14f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7aa870e2f199d6c12264fc9be86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若正项下凸数列的前
![](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/0002f427eded1721f43d60dd0fd3ffe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd419dc0a6580ab97777b2cb8fd7cded.png)
您最近一年使用:0次
2024-06-12更新
|
1137次组卷
|
5卷引用:2024届广东省三模数学试题
名校
解题方法
3 . 对于数列
,如果存在等差数列
和等比数列
,使得
,则称数列
是“优分解”的.
(1)证明:如果
是等差数列,则
是“优分解”的.
(2)记
,证明:如果数列
是“优分解”的,则
或数列
是等比数列.
(3)设数列
的前
项和为
,如果
和
都是“优分解”的,并且
,求
的通项公式.
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd84622d5883097a686797889192356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33119e0b8e033e27fde4505b90a1c3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238024e8fa2058c5cbbf2f757ce9a997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e274217ecbdfeea729eaa317359e77.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15ebc127b977d405b867a151696b163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2024-06-11更新
|
945次组卷
|
5卷引用:广东省华南师范大学附属中学2024届高三下学期5月适应性考试数学试题
名校
解题方法
4 . 在一条只能沿单向行驶的高速公路上,共有
个服务区.现有一辆车从第
个服务区向第1个服务区行驶,且当它从第
个服务区开出后,将等可能地停靠在第
个服务区,直到它抵达第1个服务区为止,记随机变量
为这辆车全程一共进入的服务区总数.
(1)求
的分布列及期望;
(2)证明:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f27f84764f1cca89ce3d93fc1cf603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dbd3cfdfc5434d53191175f7f658ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56f2ed1c214ad049f0af70377585962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bbb0a939ec3c2d0414c2351f93ae5f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570b23a0c53f8a2e896900acb8f21c03.png)
您最近一年使用:0次
2024-06-03更新
|
908次组卷
|
2卷引用:广东省广州市华南师范大学附属中学2024届高三下学期5月月考数学试题
5 . 若集合
的非空子集
满足:对任意给定的
,若
,有
,则称子集
是
的“好子集”.记
为
的好子集的个数.例如:
的7个非空子集中只有
不是好子集,即
.记
表示集合
的元素个数.
(1)求
的值;
(2)若
是
的好子集,且
.证明:
中元素可以排成一个等差数列;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f5c44de003475d3466981293cf5e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887982e3735dd7ca13293338a12df593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c469f6345826410959ea09d7e3192e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0586ec8d1d9796fb80a1250e2c0a4b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26bbb11e932ddb26a9088e7fc33e87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c562f247c1d691158f4038a030574c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68eafd45c1ec4b414d3553dabd8c2848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37765d2927d24d4b582423c843aebcd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32a859898e9905e0524d3a982eb34b6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ada01c2a8b4d92df94834a6a3929673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79df6a6d73a058d13632a726c2308d66.png)
您最近一年使用:0次
解题方法
6 . 拉格朗日中值定理是微分学的基本定理之一,其内容为:如果函数
在闭区间
上的图象连续不断,在开区间
内的导数为
,那么在区间
内存在点
,使得
成立.设
,其中
为自然对数的底数,
.易知,
在实数集
上有唯一零点
,且
.
时,
;
(2)从图形上看,函数
的零点就是函数
的图象与
轴交点的横坐标.直接求解
的零点
是困难的,运用牛顿法,我们可以得到
零点的近似解:先用二分法,可在
中选定一个
作为
的初始近似值,使得
,然后在点
处作曲线
的切线,切线与
轴的交点的横坐标为
,称
是
的一次近似值;在点
处作曲线
的切线,切线与
轴的交点的横坐标为
,称
是
的二次近似值;重复以上过程,得
的近似值序列
.
①当
时,证明:
;
②根据①的结论,运用数学归纳法可以证得:
为递减数列,且
.请以此为前提条件,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59685311c7aa9ca98b1fdbabde40171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15432e3c4e6c1d9cde98ec9187d162c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcd143a57a268a5a8ef486e2a4d5c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00108fe668a98c905f3f92b720e35a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e356055d318b6d336e9e33a1e78aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70142f9c28dc50c8ab41e71b19d18fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8488679e2fa13e44ffa5b4d802848d.png)
(2)从图形上看,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15432e3c4e6c1d9cde98ec9187d162c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15432e3c4e6c1d9cde98ec9187d162c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de261e9b4defbc0be6440397031a87b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168e68d052280fe48e1a3a6de67c6f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8559f5db9b978cb2bd290dbce7268629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a2c53e3b0b1c08803e95419f909d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87529d4cadc1e84f72d462cb8e3afac0.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1a778faac194e8de4d5178454bd04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f274881a6ad83e68c9b6652ebf4dc09.png)
②根据①的结论,运用数学归纳法可以证得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adb4f1a98a9db3b5d4e4cfc7560fdb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee28be9d207a3d3eed938484f980195.png)
您最近一年使用:0次
名校
解题方法
7 . 已知点
是抛物线
的焦点,
的两条切线交于点
是切点.
(1)若
,求直线
的方程;
(2)若点
在直线
上,记
的面积为
的面积为
,求
的最小值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a51cfe6b1f93e8beab2a1391fa5b8a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c767183fcb90fd994f705fa0bebd33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c608def11fa0e2b34f05592ef1d11fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bfbf105868ad7dca03b9663a01c3422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74b2b7a4048782fecb0126119bb5dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884d40a97fd767e95f34f3b91ab8d84c.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1e767d0df819ecd47359fee289efc3.png)
您最近一年使用:0次
2024-05-28更新
|
737次组卷
|
2卷引用:广东省广州市2024届普通高中毕业班综合测试(二)广州二模数学试卷
名校
解题方法
8 . 设抛物线C:
(
),直线l:
交C于A,B两点.过原点O作l的垂线,交直线
于点M.对任意
,直线AM,AB,BM的斜率成等差数列.
(1)求C的方程;
(2)若直线
,且
与C相切于点N,证明:
的面积不小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d0aa9412dd7caf42cc71520e282328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
(1)求C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc05c94ee6367e5551b219ac3168865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
您最近一年使用:0次
2024-05-26更新
|
3018次组卷
|
5卷引用:2024届广东省深圳市二模数学试题
2024届广东省深圳市二模数学试题(已下线)第30题 几何分析曲径通幽,代数推演水到渠成(优质好题一题多解)安徽省六安第一中学2023-2024学年高三下学期期末质量检测卷(二)数学试题(已下线)易错点8 圆锥曲线问题中未讨论直线斜率的特殊情况江西省南昌市八一中学2024届高三下学期三模测试数学试题
解题方法
9 . 有无穷多个首项均为1的等差数列,记第
个等差数列的第
项为
,公差为
.
(1)若
,求
的值;
(2)若
为给定的值,且对任意
有
,证明:存在实数
,满足
,
;
(3)若
为等比数列,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ed9652852ca4d996fd1f20808df9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b406c1887760f545f692081c10ba409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a136f516c3b52ea996c04b9989903950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd1cd7f3915a51d747e2dde3a6bf34e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499d0df6a104a5afe4ced3e1881034d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347e9a064f8636e397ee17a74d09c62f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972023813dafd940c073ab3cf09b466d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec6fb9e0625b85be3103d317fbb0cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096acdd2d0ce16e1e45397ec5e365d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd66e00bc224b433dbde6ceeaca6740.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0815e67ba8580ad64a790ade2a9957.png)
您最近一年使用:0次