设函数f(x)的定义域、值域均为R,f(x)的反函数为f
-1(x),且对于任意的x∈R,均有
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224921719145869/SYS201311012249217191458020_ST/0.png)
,定义数列{a
n},a
=8,a
1=10,a
n=f(a
n-1)(n∈N
*).
(Ⅰ)求证:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224921719145869/SYS201311012249217191458020_ST/1.png)
(n∈N
*).
(Ⅱ)设b
n=a
n+1-2a
n(n∈N
*),求证:b
n<(-6)•2
-n(n∈N
*);
(Ⅲ)是否存在常数A,B同时满足条件:
①当n=0,1时,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224921719145869/SYS201311012249217191458020_ST/2.png)
;
②当n≥2时(n∈N
*,)
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101224921719145869/SYS201311012249217191458020_ST/3.png)
.如果存在,求出A,B的值,如果不存在,说明理由.
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