Proposition: Show that for an integer $n\geq 2$, the period of the decimal expression for the rational number $\frac{1}{n}$ is at most $n-1$. I'm unsure of where to start. This is my first class on proofs. Do I state:
$\frac{1}{n}=a_n=a_1a_2...a_nb_1b_2...b_n$ with $b$ referring to the repeating part of the expression. I've looked at several other examples but am more confused than aided. I'm unsure how to prove the $n-1$ part. Any help would be appreciated.