Consider the function $f : \mathbb{R} \to \mathbb{R}$ given by $f(x) = \sqrt[3]{x + \dfrac {15} {64}}$. It has one real root at $r = -\dfrac {15} {64}$, it is increasing, convex on $(-\infty,r]$ and concave on $[r, +\infty)$. The equation $f(x) = x$ has three real roots at $\rho_1 = \dfrac {1} {8}(1-\sqrt{61})$, $\rho_2 = -\dfrac {1} {4}$ and $\rho_3 = \dfrac {1} {8}(1+\sqrt{61})$. On the other hand we have $u_{n+1} = f(u_n)$. The behaviour of $u_n$ as $n \to \infty$ depends on the starting term $u_1$, according to well-known techniques that resume to just considering the graph of $f(x)$ and its intersection with the main bisector $y=x$, and will be described by: $\bullet$ $\lim_{n \to \infty} u_n = \rho_1$ for $x \in (-\infty, \rho_2)$; $\bullet$ $\lim_{n \to \infty} u_n = \rho_2$ for $x = \rho_2$; $\bullet$ $\lim_{n \to \infty} u_n = \rho_3$ for $x \in (\rho_2, +\infty)$.