For which ordered pairs of positive real numbers $\displaystyle (a,b)$ is the limit of every sequence $\displaystyle (x_n)^{\infty}_{n=1}$ satisfying the condition $\displaystyle \lim_{n\to\infty}(ax_{n+1}-bx_n)=0$ zero?
For which ordered pairs of positive real numbers $\displaystyle (a,b)$ is the limit of every sequence $\displaystyle (x_n)^{\infty}_{n=1}$ satisfying the condition $\displaystyle \lim_{n\to\infty}(ax_{n+1}-bx_n)=0$ zero?