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

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

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

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