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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 \((10^{220} - 1)/9\).

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  • Eleventy-elevens
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  • 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 \((10^{220} - 1)/9\).
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abstract
  • 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 \((10^{220} - 1)/9\).
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