• Snazz@lemmy.world
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    1 year ago

    You can also prove it a different way if you allow the use of the formula for finding the limit of the sum of a geometric series on a non-convergent series.

    Sum(ar^n, n=0, inf) = a/(1-r)

    So,

    …999999

    = 9 + 90 + 900 + 9000…

    = 9x10^0 + 9x10^1 + 9x10^2 + 9x10^3…

    = Sum(9x10^n, n=0, inf)

    = 9/(1-10)

    = -1