Sum (i = 1..n) 9/(10^i)
this is also an infinite geometric series. If you recall, when you have an infinite geometric series, the sum equals a1 / (1 - r) where a1 = the first value in the series, and r = the ratio.
Therefore, in this case, a1 = 9/10 and r = 1/10, and thus, 0.9999rep. = 1...