题目
题型:不详难度:来源:
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074354-63547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074354-94927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074354-18212.png)
(Ⅰ)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074354-63547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074355-80449.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074355-44931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074355-78200.png)
(Ⅲ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074355-78283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074407-68732.png)
求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074407-57955.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074407-10487.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074407-75081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074355-80449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074407-57848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074408-84536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074413-39026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074413-66349.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074420-57475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074420-90024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074420-89190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074420-60272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074420-47677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074421-61909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074421-17367.png)
①-②得:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074421-23080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074407-10487.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074421-37214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074422-69613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074422-27755.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074421-37214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074422-92619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074422-96710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074423-86472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074423-71196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074423-46121.png)
(3)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074423-50020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074423-66123.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074424-54333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074424-30469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074424-11055.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074342-27042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074342-93274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074342-47027.png)
A.31 | B.32 | C.33 | D.34 |
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074312-24636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074312-85722.png)
(1)确定常数k的值,并求通项公式an;
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074312-97064.png)
已知等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074222-67459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074223-53804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074223-22752.png)
(I)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074222-67459.png)
(II)记数列
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074223-69949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074223-54863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074223-47424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074224-72674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074224-72674.png)
A.1 | B.2 | C.3 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191010/20191010074121-60213.png)
A.30 | B.170 | C.210 | D.260 |
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