# Circumscribes many notions.

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

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

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

Notation: $$a_{ij}(n)$$ denotes the element in the $$i^{\text{th}}$$ row and $$j^{\text{th}}$$ column of matrix $$A$$.

×