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Is it possible to calculate the limit $\displaystyle \lim\limits_{n \to \infty} \frac{a_n}{n}$ of the conditions?

$ a_n>0$ for $ {n \geq 1}$ and

$ a_{n-1} \leq \left(a_{n+2} - a_n \right)^n \leq a_{n+1}$.

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  • 2
    $\begingroup$ Do you have any reason to even think that there exists an infinite sequence satisfying the given inequalities? $\endgroup$ – Greg Martin Jul 21 '14 at 18:22
  • $\begingroup$ I don't know. And why has not exist? $\endgroup$ – piteer Jul 21 '14 at 18:41

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