Prove that $|x_{n+1} - x_n| \le \theta |x_n - x_{n-1}|$ for some $0 < \theta < 1$
Prove that sequence $ x_{(n+1)}= \frac {a}{1+x_n}$ is convergent to positive root of $x^2+x-a=0,$where $a >0$ and $x_1 >0$