Let \{a_{n}\}_{n=1}^{\infty}\subset R and holds
<br />
\displaystyle<br />
\lim\limits_{n\to\infty} \frac{a_{n+1}a_{n}-a_{n-1}a_{n+2}}{a_{n+1}^2-a_{n}a_{n+2}}=\alpha+\beta\ ,\quad<br />
\lim\limits_{n\to\infty}\frac{a_{n}^2-a_{n-1}a_{n+1}}{a_{n+1}^2-a_{n}a_{n+2}}=\alpha\beta\ ,\quad(|\alpha|<|\beta|)<br />
Prove that
\lim\limits_{n\to\infty}\frac{a_{n}}{a_{n+1}}=\alp  ha