Numbers

Let's define the sum of digits of a numerical sequence as the total sum of the digits of all numbers within that sequence. For instance, consider the sequence of numbers $14$, $22$, $239$. The sum of digits is calculated as (1 + 4) + (2 + 2) + (2 + 3 + 9) = 23.

Your task is to determine the sum of digits for the following numerical sequence given a specific $n$:

1, 2, 3, \ldots, 10^n - 1