Recurring Styles 4 - Limit of an Expression!

Calculus Level 5

\[\large{\lim_{n \to \infty} \dfrac{x_n \cdot x_{n+2}}{x_{n+1}^2} = 4}\]

Let \((x_n)_{n=1}^{\infty}\) be a sequence such that the above limit satisfies, and where \(x_i > 0\) for every \(i \geq 1\). Then find the value of \( \displaystyle {\lim_{n \to \infty} \sqrt[n^2]{x_n} }\).

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