Find $\lim\limits_{n\to\infty}\left(\frac{a_1}{a_2}+\frac{a_2}{a_3}+\frac{a_3}{a_4}+...+\frac{a_n}{a_1}\right)$ if {$a_n$} is random sequence with positive terms.
If sequence is increasing ($a_1>a_2>...>a_n$), then $L=+\infty$
What is the limit when sequence is decreasing?
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