Sunday, 24 November 2013

calculus - Limit of a Recursive Sequence

I'm having a really hard time finding the limit of a recursive sequence -



a(1)=2,a(2)=5,a(n+2)=12(a(n)+a(n+1)).




I proved that the sequence is made up from a monotonically increasing sequence and a monotonically decreasing sequence, and I proved that the limits of the difference of these sequences is zero, so by Cantor's Lemma the above sequence does converge. I manually found out that it converges to 4, but I can't seem to find any way to prove it.



Any help would be much appreciated!
Thank you.

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