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Topic: Limit of recursive sequence (a_1=1, a_2=3, a_n=weighted average of previous
Replies: 2   Last Post: Dec 12, 2011 1:28 PM

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hobbit.trap

Posts: 3
Registered: 11/2/11
Limit of recursive sequence (a_1=1, a_2=3, a_n=weighted average of previous
Posted: Nov 2, 2011 9:34 PM
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a_1 = 1
a_2 = 3

For n>2, a_n = (a_{n-2} + 2*a_{n-1}) / 3

(Rendering: http://mathbin.net/78948)

It's easy to show that a_n does converge using the nested interval theorem. I used Maxima to see that the limit is 2.2, but I'd like to see analytically why the limit is 2.2? The "usual" method of saying a=(a+2a)/3 fails, since that's a tautology.



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