我们规定:对于任意实数A,若存在数列{a
n}和实数x(x≠0),使得A=a
1+a
2x+a
3x
2+…+a
nx
n-1,则称数A可以表示成x进制形式,简记为:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183159224717188/SYS201310241831592247171019_ST/0.png)
.如:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183159224717188/SYS201310241831592247171019_ST/1.png)
,则表示A是一个2进制形式的数,且A=-1+3×2+(-2)×2
2+1×2
3=5.
(1)已知m=(1-2x)(1+3x
2)(其中x≠0)),试将m表示成x进制的简记形式.
(2)若数列{a
n}满足a
1=2,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183159224717188/SYS201310241831592247171019_ST/2.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183159224717188/SYS201310241831592247171019_ST/3.png)
(n∈N
*).求证:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183159224717188/SYS201310241831592247171019_ST/4.png)
.
(3)若常数t满足t≠0且t>-1,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183159224717188/SYS201310241831592247171019_ST/5.png)
,求
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183159224717188/SYS201310241831592247171019_ST/6.png)
.
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