题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060039-94431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060039-56773.gif)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-22292.gif)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-84842.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-90633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-71185.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-61159.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-97337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-21435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060041-71591.gif)
解答下列问题:
(Ⅰ)证明数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060041-16593.gif)
(Ⅱ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060041-21708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060041-22520.gif)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060042-75477.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060042-21507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060042-70090.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-61159.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060042-52913.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060040-21435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060042-44455.gif)
所以不论哪种情况,都有
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060043-10129.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060043-55431.gif)
故数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060043-64727.gif)
(Ⅱ)由(Ⅰ)知,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060043-55158.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060044-79157.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060044-71343.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060044-72032.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060044-18350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060044-37684.gif)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060042-21507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060045-18439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060045-97094.gif)
由②知
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060045-25865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060045-51810.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060046-91525.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060046-72638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060046-64103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060046-76367.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060046-63271.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060047-35288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060047-37527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060047-60609.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060047-46724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060042-21507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060045-18439.gif)
因此n是满足
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060048-99119.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060048-67203.gif)
因而,n是满足
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060048-58432.gif)
解析
核心考点
试题【(本小题满分14分)数列和数列由下列条件确定:①;②当时,与满足如下条件:当时,;当时,。解答下列问题:(Ⅰ)证明数列是等比数列;(Ⅱ)求数列的前n项和为;(Ⅲ】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060025-21913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060026-44568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060026-50828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060026-94682.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060026-67249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060026-94617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060026-85289.gif)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060025-21913.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060027-42908.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060027-87902.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060027-65761.gif)
(Ⅲ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060027-86869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060028-55623.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060028-73375.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060026-94682.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060028-40782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060028-38357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060028-58439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060029-27128.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060029-33969.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060014-10069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013060008-88903.gif)
(1)求点Pn的纵坐标bn的表达式;
(2)若对于每个自然数n,以bn,bn+1,bn+2为边长能构成一个三角形,求a的取值范围;
(3)设Cn=lg(bn)(n∈N*),若a取(2)中确定的范围内的最小整数,问数列{Cn}前多少项的和最大?试说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055951-28139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055951-34880.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055951-77309.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055951-27007.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055951-28139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055951-51570.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055952-41858.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055952-16865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055938-28132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055939-11609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055939-15947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055939-42424.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055939-11609.png)
(2)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055939-43121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055939-51222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055940-24722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055940-38850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055940-54665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191013/20191013055940-41292.png)
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