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


a_1 = 1 a_2 = 3
For n>2, a_n = (a_{n2} + 2*a_{n1}) / 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.



