Eleventy-elevens is a positive integer formed by concatenating 110 (eleventy) copies of the digits "11." Its decimal representation is: 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 By expressing this number as a partial sum of the geometric series 1 + 10 + 100 + ..., we can derive a simple closed-form expression \((10^{220} - 1)/9\).