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   Author  Topic: Alternating arithmetic and geometric means  (Read 881 times)
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Alternating arithmetic and geometric means  
« on: Jun 17th, 2010, 1:40am »		 Quote Quote Modify Modify
Define a sequence by t0 = 0, t1 = 1, and for n>1
tn = (1/2)(tn-1 + tn-2) for even n;
tn = sqrt(tn-1 * tn-2) for odd n.
 
Find the limit of tn as n goes to infinity.
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Re: Alternating arithmetic and geometric means  
« Reply #1 on: Jun 17th, 2010, 4:29am »		 Quote Quote Modify Modify
It looks a bit like it might be formula (65) @ http://mathworld.wolfram.com/PiFormulas.html, but although the value matches, it doesn't seem to work out.
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Re: Alternating arithmetic and geometric means  
« Reply #2 on: Jun 17th, 2010, 10:11am »		 Quote Quote Modify Modify
The value is, of course, correct, but I agree that that particular formula doesn't seem to work out here.
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