If \[a(x,y)=1+\dfrac{x^2}{y^2}, \ x \in \mathbb{N}, \ y \in \mathbb{N}\] then find the value of \[\lim_{n \rightarrow \infty} \prod_{k=1}^{n} \sqrt[n]{a(k,n)}\]

**Details and Assumptions**

\(\bullet \ \ \displaystyle\prod_{r=1}^{n} a_r=a_1 \cdot a_2 \cdot a_3 \ ..... \ a_n\)

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