Limit of a sequence (3)

Calculus Level 5

If a(x,y)=1+x2y2, xN, yNa(x,y)=1+\dfrac{x^2}{y^2}, \ x \in \mathbb{N}, \ y \in \mathbb{N} then find the value of limnk=1na(k,n)n\lim_{n \rightarrow \infty} \prod_{k=1}^{n} \sqrt[n]{a(k,n)}

Details and Assumptions

  r=1nar=a1a2a3 ..... an\bullet \ \ \displaystyle\prod_{r=1}^{n} a_r=a_1 \cdot a_2 \cdot a_3 \ ..... \ a_n

Also try limit as a sequence (1) and (2).

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