2010·重庆·一模
解题方法
1 . 已知函数
,满足:①对任意
,都有![](https://img.xkw.com/dksih/QBM/2010/6/5/1569755385888768/1569755391262720/STEM/e5aec372eca147b5bc4e2dc8afb58d52.png?resizew=143)
;
②对任意n∈N *都有
.
(Ⅰ)试证明:
为
上的单调增函数;
(Ⅱ)求
;
(Ⅲ)令
,试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604c3ed013411e9434f9b09044231465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2c2b34f9a5a85e9e2d4057b3c10130.png)
![](https://img.xkw.com/dksih/QBM/2010/6/5/1569755385888768/1569755391262720/STEM/e5aec372eca147b5bc4e2dc8afb58d52.png?resizew=143)
![](https://img.xkw.com/dksih/QBM/2010/6/5/1569755385888768/1569755391262720/STEM/61c06d7e06ef4e06b116740ee0d6ec6c.png?resizew=53)
②对任意n∈N *都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407169706c508bfae5d039639b49477d.png)
(Ⅰ)试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd62e0e1189886f90e0c5bc126f64a4.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cf16d7b4f5f2f8d6a1fe2d8a59538b.png)
(Ⅲ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2f851b643e3a77682f0196dcf3e797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fe881244327001ef94b611e6b159db.png)
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