题目
题型:不详难度:来源:
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103338-78735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103338-70089.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103338-79178.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103339-65072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103339-81728.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103345-33891.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103345-89034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103345-28095.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103345-73102.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103346-97108.gif)
(I)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103338-78735.gif)
(II)求证:数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103346-83357.gif)
(III)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103345-89034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103346-13359.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103346-93273.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103347-16836.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103347-87707.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103347-15330.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103347-98735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103345-73102.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103348-93393.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103348-94464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103348-24852.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103348-40311.gif)
可证
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103348-45161.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103349-33201.gif)
∴数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103346-83357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103349-87878.gif)
(3)由(2)得
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103349-83610.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103349-99709.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103350-52266.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103350-40119.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103345-89034.gif)
当n=1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103345-28095.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103350-57321.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103350-16856.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103351-23963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103351-36056.gif)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103351-76946.gif)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103323-42656.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103323-81470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103323-61765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103323-40669.gif)
A.![]() ![]() ![]() | B.8 | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103309-19585.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103309-99108.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103310-49163.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103310-53827.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103310-21602.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103310-84339.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103311-80723.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103303-52383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103303-47771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103303-50012.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103304-49799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103303-52383.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103234-95809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103234-37749.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103234-37749.gif)
设数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-25134.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-30082.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-40683.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-49527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-29578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-76663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-22786.gif)
(Ⅰ) 求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-25134.gif)
(Ⅱ)当m=1时,求
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-50763.gif)
(Ⅲ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-28441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103235-25134.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103236-19750.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103236-19750.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103236-22115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103236-17961.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103211-83362.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103211-54040.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103211-47787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103212-79096.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103212-69291.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103212-41048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191011/20191011103212-75834.gif)
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