So my problem is: given $x_{n+1}=(x_{n})^3+(x_{n})^{1/3}$ and $x_0=1$, prove or disprove the following statement: it is possible to find a closed form of this.
I am very confused how to do this: should I proceed by induction? I know how to find the rate for how fast this thing increase( but not in close form)-- I want to know if this is even possible to write in closed form...