0.99999... = 9/10 + 9/100 + 9/1000 + ...
           = 9*( 1/10 + 1/100 + 1/1000 + ... )
           = 9*sum( (1/10)^n, n=1..inf )
           = 9*(1/(1 - 1/10)-1)  #geometric series sum
           = 9*(10/9 - 1)
           = 9*(1/9)
           = 1
QED