数列{a
n}的前n项和S
n满足S
n-S
n-1=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231010862128846/SYS201311012310108621288018_ST/0.png)
+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231010862128846/SYS201311012310108621288018_ST/1.png)
(n≥2),a
1=1.
(1)证明:数列
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231010862128846/SYS201311012310108621288018_ST/2.png)
是等差数列.并求数列{a
n}的通项公式;
(2)若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231010862128846/SYS201311012310108621288018_ST/3.png)
,T
n=b
1+b
2+…+b
n,求证:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231010862128846/SYS201311012310108621288018_ST/4.png)
.
考点分析:
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231010862128846/SYS201311012310108621288015_ST/4.png)
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如图所示的螺旋线是用以下方法画成的,△ABC是边长为1的正三角形,曲线CA
1,A
1A
2,A
2A
3分别是A,B,C为圆心,AC,BA
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2A
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231010862128846/SYS201311012310108621288013_ST/0.png)
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231010862128846/SYS201311012310108621288013_ST/1.png)
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