Twelvety-twelves is a positive integer formed by concatenating 120 (twelfty) copies of the digits "12." Its decimal representation is: 121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212 By expressing this number as a partial sum of the geometric series 12 + 1200 + 120000 + ..., we can derive a simple closed-form expression \(12(100^{120} - 1)/99\).