Circumscribes many notions.

Let [2110]n=(aij(n)) \left[ \begin{matrix} 2 & 1 \\ 1 & 0 \end{matrix} \right]^n=\left( a_{ij}(n) \right)

If (limna12(n)a22(n))2=A+B(A,BN) \left( \displaystyle \lim_{n \to \infty} \dfrac{a_{12}(n)}{a_{22}(n)} \right)^2=\sqrt{A}+\sqrt{B} \quad \quad \left( A,B \in \mathbb{N}\right)

then find the value of A+B A+B .

Notation: aij(n)a_{ij}(n) denotes the element in the ithi^{\text{th}} row and jthj^{\text{th}} column of matrix AA.

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