Sorry for all the questions but if there is a recurrence relation such that $\displaystyle x_{1} =1$, and for $\displaystyle n \ge 1, x_{n+1} = 3x_{n}^{2}$, how do I show that $\displaystyle \lim_{n\to \infty}\,(x_{n})$ does not exist. It is obvious, but I do not know how to show it. I'm assuming there is a general formula for this recurrence relation but I cannot find it. Or is there another way to prove it altogether?