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November 2nd, 2013, 12:56 PM  #1 
Newbie Joined: Nov 2013 Posts: 1 Thanks: 0  Total area of circle using sequences and or series
How do I find the total area of total area of the red circles C_n,n=1,2,3? I am very confused with this problem. I have been working on it for about an hour and still nothing . Help would be greatly appreciated! I know that I can use sequences to solve this problem, however, I am confused on how to approach it. I pasted a url that displays the picture of my question. http://tinypic.com/r/2dkmmq1/5 
November 2nd, 2013, 03:25 PM  #2 
Senior Member Joined: Jul 2011 Posts: 118 Thanks: 0  Re: Total area of circle using sequences and or series
For the first circle we have: For the next ones the formula is: First few results are: So we can guess that: It is easy to show that by induction: 

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