You can learn why is that on Wikipedia: en.wikipedia.org/wiki/0.999...

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If you flip a coin once, the probability that it will come up head is 1/2.
When you flip it twice, you get: 1/2 x 1/2 = 1/4

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5^(-1) = (1/5)^1 = 1/5

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n = 100
2 x 100 - 1 = 199

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