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November 2nd, 2013, 12:56 PM   #1
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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
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November 2nd, 2013, 03:25 PM   #2
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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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