$\{{x_n}\}_{n \geq 1}$ be a sequence such that $|x_{n+1} - x_n| \leq \frac{1}{2} |x_n - x_{n-1}|.$ Prove ${x_n}$ is convergent
$\left|x_{n+1} - x_n\right| < C\left|x_n - x_{n-1}\right|$ prove this is Cauchy