Try to prove that if it is \(\displaystyle 0.a_1 a_2 a_3 ... a_n a_1 a_2 a_3 ... a_n a_1 a_2 a_3 ... a_n ... \)then it can be writen as a fraction : \(\displaystyle \frac{ a_1 a_2 a_3 ... a_n}{999...9} \) or \(\displaystyle \frac{ a_1 a_2 a_3 ... a_n}{ 10^n - 1 } \)