2011·湖北·一模
1 . 已知数列
满足:
,已知存在常数
使数列
为等比数列.
(1)求常数
及
的通项公式;
(2)解方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de01e0ca0018abba2aec23cc20464a62.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a3c61223aeb2841f2cef0e9168e42b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a296a9dc44a92a470f4026827a1a9d.png)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de01e0ca0018abba2aec23cc20464a62.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d456c6fa7282e4126b10a47ec0afb6de.png)
您最近一年使用:0次
2011·福建泉州·三模
2 . 设
,
(1)分别求出满足
的
,并猜想
的表达式;
(2)用数学归纳法证明:(1)中猜想所得的
使得等式
对于大于1的一切自然数
都成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f9478be570bbd7390eceedc64021ca.png)
(1)分别求出满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de87e295fcdfbb169df8c5057a7543a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9233bb9ce4e0c5bf17b9d4d2ddb929e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
(2)用数学归纳法证明:(1)中猜想所得的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de87e295fcdfbb169df8c5057a7543a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2011·江苏淮安·模拟预测
解题方法
3 . 已知
,(其中
)
.
(1)求
;
(2)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafd0aacdcbc234414cc24ef45a93eeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9158db048850992ae4cace688253bf4c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5fb802bea8359d042dfd7d9a8cedcb.png)
您最近一年使用:0次