题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084304-89809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084304-94927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084304-38188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084305-68071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084304-94927.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084305-85712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084311-57156.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084311-58644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-43722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084304-94927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-16867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084304-94927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-16867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-16867.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-31596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-62299.png)
(2),n=7时,Tn取得最大值,且Tn的最大值为 T7=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084313-11219.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084313-55255.png)
再令n=2可得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084313-50070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084305-85712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084311-57156.png)
(2)在(1)的基础上,可知
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-31596.png)
再根据
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084313-33314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084314-28454.png)
所以an=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084314-61264.png)
据此可知{an}是等比数列,因而
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084314-55719.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084314-98545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084315-90894.png)
取n=1,得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084313-55255.png)
取n=2,得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084313-50070.png)
又②-①,得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084315-11250.png)
(1)若a2="0," 由①知a1=0,
(2)若a2
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084315-71775.png)
由①④得:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-31596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-62299.png)
(2)当a1>0时,由(I)知,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084312-31596.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084313-33314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084314-28454.png)
所以,an=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084314-61264.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084314-55719.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084315-58170.png)
所以,数列{bn}是以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084315-90894.png)
则 b1>b2>b3>>b7=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084315-50869.png)
当n≥8时,bn≤b8=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084316-80114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084316-84456.png)
所以,n=7时,Tn取得最大值,且Tn的最大值为
T7=
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084313-11219.png)
核心考点
举一反三
已知正项等差数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084239-67719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084239-79728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084239-16846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084239-50585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084239-59607.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084239-67719.png)
(2)记
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084240-62041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084239-79728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084240-54665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084240-27188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084221-53178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084221-37592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084221-21809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084222-36280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084222-64205.png)
(Ⅰ)若{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084222-93453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084222-20094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084222-64205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084223-11615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084223-13705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084223-73673.png)
(Ⅱ)设数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084223-13933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084223-86743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084224-68607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084222-36280.png)
(Ⅲ)设数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084224-73837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084224-84664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084224-97138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084215-22630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084216-11791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084216-46208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084216-97100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084217-11827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084217-42613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084217-83546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084217-64238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084217-47542.png)
A.55 | B.70 | C.85 | D.100 |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084213-88789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084213-43499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084213-94916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084145-51004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084145-69243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084145-62286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084156-18124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084156-71728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084157-81596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084157-60471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084157-76873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084145-69243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084158-37657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084158-15918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012084158-86842.png)
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