Let x be a real number which as a recurring decimal expansion


so that there exsit positive integers N and k such that a(subscript)(n+k)=a(subscrpit)n for all n>N. show that

x= (b/10^N)+{c/(10^N)[(10^k)-1]}

where b and c are integers to be found. Deduce that x is rational.

Help will be greatly appreciated as it need to be in tomorrow afternoon. Thanks.