调研卷子21题请教:
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/18 07:27:31
调研卷子21题请教:
![](http://img.wesiedu.com/upload/3/21/321a25bb107dfe63e5a711909fe5cf38.jpg)
请老师一定帮忙解答,非常感谢!
![](http://img.wesiedu.com/upload/3/21/321a25bb107dfe63e5a711909fe5cf38.jpg)
请老师一定帮忙解答,非常感谢!
解题思路: 用不完全归纳法猜测结论,用数学归纳法进行证明.。 第二问的运算很复杂,不知道有没有错误(若有错误,则证明可能就失效了)请替我检查一下.
解题过程:
证明(法一):(1) 首先,由
,
, 可得
,又由
, 可得
,由
,
,知
是首项为2、公比为4的等比数列, ∴
;…………………………………………①由
,
,知
是首项为4、公比为4的等比数列, ∴
;……………………………………………②由①②,得
, 从而,
,∴ 数列{
}是公比为2 的等比数列; (法二):首先,由
,
, 可得
,猜想:
(
),下面用数学归纳法证明:①当n=1时已经成立; ② 假设n=k(
)时成立,即
,则 由
,得
, 即n=k+1时也成立,∴ 对一切正整数n,都有
,(下同证法一); (2) 承(1),由题意得
, ∴
,又∵
,∴
欲证
, 等价于
,下面,我们用数学归纳法证明
,①
<
,显然成立;② 假设
, 则:∵ 对号函数
在
上是增函数,∴
,只需证
,
,
,
,
,
,
,
,
,
, 最后这个式子显然成立,∴
成立,由①②,据数学归纳法原理得
总成立,∴
恒成立.
解题过程:
![](http://img.wesiedu.com/upload/9/f1/9f17078ceb113896d558cfc6f0449f86.jpg)
![](http://img.wesiedu.com/upload/4/0f/40fc02e6b7b469b305c4364e86be16eb.gif)
![](http://img.wesiedu.com/upload/5/75/57541d2069fa8624bbaa0382ff6aff1e.gif)
![](http://img.wesiedu.com/upload/f/04/f0406549efc1d01c58012afad4531f7b.gif)
![](http://img.wesiedu.com/upload/f/24/f241a0da8d00df1344dbde31dc1b123b.gif)
![](http://img.wesiedu.com/upload/f/44/f44507d670eeaafa872603413fb97d13.gif)
![](http://img.wesiedu.com/upload/4/0f/40fc02e6b7b469b305c4364e86be16eb.gif)
![](http://img.wesiedu.com/upload/6/4e/64ecd257dc1b40c84c48049ef6fbd46a.gif)
![](http://img.wesiedu.com/upload/8/57/857caf1ed6671b2efd750a973a3f6a69.gif)
![](http://img.wesiedu.com/upload/2/6b/26b7f70fdcf5442231d1f0fb6989f814.gif)
![](http://img.wesiedu.com/upload/f/04/f0406549efc1d01c58012afad4531f7b.gif)
![](http://img.wesiedu.com/upload/7/a1/7a1a4541d66f2e0c68d87c8d8e480be4.gif)
![](http://img.wesiedu.com/upload/1/c0/1c023ef940bf8c5f2b1760180f99a833.gif)
![](http://img.wesiedu.com/upload/c/05/c0590b0d650e788a5dc3fb0b9cac89e9.gif)
![](http://img.wesiedu.com/upload/4/02/4025df0ba7b325a9fe5d5fb56eb5a23b.gif)
![](http://img.wesiedu.com/upload/9/84/9841e3a6a2c6d2ada462c05cd4441e9a.gif)
![](http://img.wesiedu.com/upload/6/b3/6b38c1fd0e70b34f70617047d23bf6b4.gif)
![](http://img.wesiedu.com/upload/4/0f/40fc02e6b7b469b305c4364e86be16eb.gif)
![](http://img.wesiedu.com/upload/5/75/57541d2069fa8624bbaa0382ff6aff1e.gif)
![](http://img.wesiedu.com/upload/f/04/f0406549efc1d01c58012afad4531f7b.gif)
![](http://img.wesiedu.com/upload/4/02/4025df0ba7b325a9fe5d5fb56eb5a23b.gif)
![](http://img.wesiedu.com/upload/3/04/30406c5ab3b4c532d2453ae9d0c8a8b0.gif)
![](http://img.wesiedu.com/upload/e/24/e248277a416e0a942278ae92cecd7f08.gif)
![](http://img.wesiedu.com/upload/c/c9/cc975e73ac28f32c999f88e652fe2c6a.gif)
![](http://img.wesiedu.com/upload/b/90/b90021cc6c3a3dcfcbedd75fa7e5444e.gif)
![](http://img.wesiedu.com/upload/1/cf/1cf4e634d3193795489c5ed0826253ba.gif)
![](http://img.wesiedu.com/upload/4/02/4025df0ba7b325a9fe5d5fb56eb5a23b.gif)
![](http://img.wesiedu.com/upload/6/e0/6e05a1da99f05526b17a498fb8962719.gif)
![](http://img.wesiedu.com/upload/0/1c/01c95f6094fe26b60c4e035de9d4ab0c.gif)
![](http://img.wesiedu.com/upload/3/81/3811ce6220d01e489141542471639229.gif)
![](http://img.wesiedu.com/upload/d/e8/de8ed289321786a9023b16fc9950c091.gif)
![](http://img.wesiedu.com/upload/6/ba/6bad08a6e8742762b64650c64fbe64a7.gif)
![](http://img.wesiedu.com/upload/3/e8/3e892504d2c89daf3264a03287d6c969.gif)
![](http://img.wesiedu.com/upload/9/ba/9ba624d4b7a5cf1f4776b554b53421fa.gif)
![](http://img.wesiedu.com/upload/3/81/3811ce6220d01e489141542471639229.gif)
![](http://img.wesiedu.com/upload/4/b9/4b92be4f29709163ed0b4bed92b6e196.gif)
![](http://img.wesiedu.com/upload/c/6d/c6d768fe9f781a6c3a48813ecbad5e4e.gif)
![](http://img.wesiedu.com/upload/b/62/b62914e52798c66deb1d4514fab92fb1.gif)
![](http://img.wesiedu.com/upload/7/25/7252204a55be160db1cb8228f733c393.gif)
![](http://img.wesiedu.com/upload/5/51/551bcd4f2ed030462bf339bcfc468054.gif)
![](http://img.wesiedu.com/upload/0/e3/0e357fe2258e9a8f606c88e7097377a3.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/3/27/3278cff437287ad983e6c936c47c4efe.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/e/82/e820dd4bec04018972f09bdd15a3ce5a.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/e/ea/eeaa4fd807a37e5df332eb2ce5ea0c94.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/9/ed/9ed6975d29528d4eaf6c8664a8787a33.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/7/8c/78c3ea3fa47d4fa420bac475ccd78fea.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/9/8d/98d3b9952e224fa701ec21fc1226484d.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/7/a9/7a95ad66f228d9c03f039e2377de34e8.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/9/71/971fe6321ce98b7113646877507a2c71.gif)
![](http://img.wesiedu.com/upload/7/26/726205a926943dd6c67792c2d79a4a94.gif)
![](http://img.wesiedu.com/upload/4/68/468f5bbbb403cd0853a14ba152647426.gif)
![](http://img.wesiedu.com/upload/2/4f/24fcab38ea5ab2306df3111017407280.gif)
![](http://img.wesiedu.com/upload/9/ba/9ba624d4b7a5cf1f4776b554b53421fa.gif)
![](http://img.wesiedu.com/upload/b/c6/bc676c9df8ff1c1a5969088be9dc6c39.gif)