Chapter 5.4, Problem 34ES

It is a fact that every integer $n\ge 1$ can be written in the from $c_r,3^r+c_{r-1},3^{r-1}+\mathrm{...}+c_2,3^2+c_1,3+c_0,$

where $c_r=1$ or and $c_i=0,1,$ or 2 for each integer $i=0,1,2,\mathrm{...},r-1$ . Sketch a proof of this fact.