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