题目
题型:不详难度:来源:
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072154-33968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-38992.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-22916.gif)
且对任意m,n∈
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-10968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-92824.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-70988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072156-14022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072156-29907.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072156-75141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072156-11084.gif)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-22568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-66255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-70988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-10968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-10387.gif)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-48718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-27934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-92427.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-33565.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-10968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-44857.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072156-75141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-84402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-38992.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072156-11084.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-81318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-38992.gif)
(2)当n∈
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-10968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072159-17377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-70988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072159-97840.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072159-40933.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072159-15655.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-66255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-70988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072200-48820.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-22568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-10387.gif)
(3)由(1)(2)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-10387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072200-78021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072156-75141.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-38992.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-22568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-66255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072155-70988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-92427.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072200-89479.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072200-64496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-27934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-92427.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072201-22067.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072201-86154.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072157-48718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072201-46022.gif)
当q=1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-44857.gif)
当q≠1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-44857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072201-46036.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072201-25146.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072202-58939.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-33565.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072202-47004.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072201-25146.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072202-58939.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072202-17970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072202-29928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072203-51027.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072203-37877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072202-29928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072203-95069.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072202-29928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072204-52112.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-44857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072204-50446.gif)
综上所述,
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072158-44857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072204-61325.gif)
解析
核心考点
试题【(本小题满分16分)已知数列满足=0,=2,且对任意m,n∈都有+=+(1)求,;(2)设=-( n∈),证明:是等差数列;(3)设=(-)( q≠0,n∈),】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072134-86378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072134-36064.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072134-73501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072135-67192.gif)
(1)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072134-86378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072135-64495.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072135-64495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072134-86378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072135-65275.gif)
(3)若对任意n∈
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072135-67192.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072135-35883.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072135-64495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072123-20915.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072123-76957.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072123-14147.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072124-81124.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072124-39302.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072124-11595.gif)
A.96 | B.99 | C.100 | D.101 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072111-68399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072117-40060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072117-48718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072111-68399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072118-94618.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072118-59921.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072103-98964.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072103-33406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072104-54303.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072104-60687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072104-72166.gif)
A.12 | B.18 | C.24 | D.42 |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072043-93087.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072043-27011.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072043-11978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011072043-33629.gif)
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