题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082554-14756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082554-43716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082554-37704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082555-75912.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082555-10784.png)
(1)求r的值; (4分)
(2)当b=2时,记
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082555-36225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082555-55972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082555-60274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082555-78190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082556-37840.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082556-31352.png)
解析
(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082554-37704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082556-75131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082556-40710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082557-86639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082557-32014.png)
(2)由(1)得等比数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082554-14756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082608-97692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082608-39814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082608-51292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082608-55762.png)
解:(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082554-37704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082556-75131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082556-40710.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082557-86639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082609-40149.png)
又因为{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082554-14756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082556-31352.png)
(2)证明:
由(1)得等比数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082554-14756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082608-97692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082608-39814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082608-51292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082608-55762.png)
当b=2时,
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082609-30824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082609-41938.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082609-69870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082610-41524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082610-24880.png)
两式相减, 得
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082610-17842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082610-16809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082611-25459.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082611-86966.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082558-93004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082558-94758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082559-73701.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082558-93004.png)
(2)若数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082558-93004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082559-14132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082559-39906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082559-14132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082457-55237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082457-70458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082457-68847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082457-21729.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082457-55237.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082458-49135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082458-96603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082458-84940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082449-70634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082449-39721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082449-56669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082449-84207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082450-49353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082450-21146.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082439-45156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082439-39863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082440-94899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082440-82425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082440-67041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082440-25413.png)
已知数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082416-30779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082417-25694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082417-73358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082417-63802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082417-85921.png)
(1)确定
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082418-26725.png)
(2)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082416-30779.png)
(3)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082418-16010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082417-25694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191012/20191012082418-78640.png)
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