power series.
0.999... = sigma 9/10^n n=1 -> inf = 9 * sigma 1/10^n n=1 -> inf = 9 * ((sigma 1/10^n n=0 -> inf) - 1) =
power series sigma 1/10^n n=0 -> inf = 1/(1-1/10)
= 9 * (1/(1-1/10) - 1) = 1
qed.
0.999... = sigma 9/10^n n=1 -> inf = 9 * sigma 1/10^n n=1 -> inf = 9 * ((sigma 1/10^n n=0 -> inf) - 1) =
power series sigma 1/10^n n=0 -> inf = 1/(1-1/10)
= 9 * (1/(1-1/10) - 1) = 1
qed.
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