The explanation I’ve seen is that … is notation for something that can be otherwise represented as sums of infinite series.

In the case of 0.999…, it can be shown to converge toward 1 with the convergence rule for geometric series.

If |r| < 1, then:

ar + ar² + ar³ + … = ar / (1 - r)

Thus:

0.999… = 9(1/10) + 9(1/10)² + 9(1/10)³ + …

= 9(1/10) / (1 - 1/10)

= (9/10) / (9/10)

= 1

Just for fun, let’s try 0.424242…

0.424242… = 42(1/100) + 42(1/100)² + 42(1/100)³

= 42(1/100) / (1 - 1/100)

= (42/100) / (99/100)

= 42/99

= 0.424242…

So there you go, nothing gained from that other than seeing that 0.999… is distinct from other known patterns of repeating numbers after the decimal point.