设 $a>0$, $$\bex x_1=1,\quad x_{n+1}=x_n+an\prod_{i=1}^n x_i^{-\frac{1}{n}}. \eex$$ 试证: $$\bex \vlm{n}x_n=\infty,\quad \vlm{n}\frac{x_n}{\ln n}=\infty. \eex$$
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