解:(Ⅰ)将直线y=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109106267.gif)
x的倾斜角记为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109121200.gif)
,
则有tan
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109121200.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109137268.gif)
,sin
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109121200.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316310916873.gif)
.………….1分
设Cn的圆心为(
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109184310.gif)
,0),则由题意知
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109199364.gif)
= sin
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109121200.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316310916873.gif)
,
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109184310.gif)
= 2
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109277211.gif)
; ……… ………….3分
同理
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109511428.gif)
,依题意知
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109823591.gif)
………………5分
将
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109184310.gif)
= 2
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109277211.gif)
代入,
解得 rn+1=3rn.
故{ rn }为公比q=3的等比数列. ………………7分
(Ⅱ)由于r1=1,q=3,故rn=3n-1,从而
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109886371.gif)
=n·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109090226.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316310991785.gif)
,………………9分
记Sn=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109948576.gif)
,
则有 Sn=1+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316310997972.gif)
2·3-1+3·3-2+………+n·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109090226.gif)
. ①
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163110026273.gif)
=1·3-1+2·3-2+………+(n-1) ·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109090226.gif)
+n·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163110057215.gif)
. ② ………………11分
①-②,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163110089401.gif)
="1+3-1" +3-2+………+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109090226.gif)
-n·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163110057215.gif)
…
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316311013572.gif)
……………………12分
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163110167438.gif)
- n·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163110057215.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163110198224.gif)
–(n+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109075223.gif)
)·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163110057215.gif)
………………………………13分
Sn=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109059236.gif)
–
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109075226.gif)
(n+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109075223.gif)
)·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163109090226.gif)
. ………………………………14分
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231631103545422.gif)