Prove that every positive rational number can be expressed uniquely in the form [tex]\sum^{n}_{k=1} \frac{a_k}{k!}[/tex] where [tex]a_1 , a_2, a_3, \cdots a_n[/tex] are integers such that [tex]0 \leq a_n \leq n-1[/tex] for all [tex]n\ \textgreater \ 1[/tex].