Recurring Styles 4 - Limit of an Expression!

Calculus Level 5

limnxnxn+2xn+12=4\large{\lim_{n \to \infty} \dfrac{x_n \cdot x_{n+2}}{x_{n+1}^2} = 4}

Let (xn)n=1(x_n)_{n=1}^{\infty} be a sequence such that the above limit satisfies, and where xi>0x_i > 0 for every i1i \geq 1. Then find the value of limnxnn2 \displaystyle {\lim_{n \to \infty} \sqrt[n^2]{x_n} }.

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