Without getting formal about the proof:

1..9 = 45
1..99 = SumOfTensDigits + SumOfOnesDigits
    = 10*1..9 + 10*1..9 = 900
1..999 = SumOfHundredsDigits + SumOfTensAndOnesDigits
    = 100*1..9 + 10*1..99 = 4500 + 9000 = 13500
1..9999 = 1000*1..9 + 10*1..999 = 45000 + 135000 = 180000
...
1..'9'x$n
    = 45, 450+450, 4500 + 4500+4500, 45000 + 3*45000, ...
    = 4.5*$n*10^$n
1..1e6 = 1..'9'x6 + 1 = 4.5*6*10^6 + 1 = 27e6 + 1
    = 27_000_001
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