Let $x_1=2,x_{n+1}=\ln|x_n|$, prove $z=\lim_{n\rightarrow+\infty}\frac{1}{n}\sum_{k=1}^nx_k$ exist and $z=\ln(-z)$.

June 8, 2024, 1:31 am

Let $x_1=2,x_{n+1}=\ln|x_n|$, prove $$z=\lim_{n\rightarrow+\infty}\frac{1}{n}\sum_{k=1}^nx_k$$exist and $z=\ln(-z)$.

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