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Let

A_0 = 6

A_1 = 5

A_n = A_(n-1)  + A_(n-2) for n ≥ 2

There is a unique ordered pair (c,d) such that \(c\phi^n + d\widehat{\phi}^n\) is the closed form for A_n. Find c using the Fibonacci and Lucas number sequences.

 Mar 16, 2021
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Taking the limit, we get that c = 4 - sqrt(5).

 Mar 16, 2021

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