31 Mar
2011
31 Mar
'11
9:47 a.m.
If we carry on, this appears to be converging to 1/81, which is the lovely repeating decimal 0.0123456790123456790...
Indeed, it does: 111 ... 111 = (10^x-1)/9 8999 ... 999 = 9*10^x-1 Ratio = (10^x-1)/(81*10^x-9) As only the 10^x terms are significant, the ratio approaches 1/81. Sincerely, Adam P. Goucher