Concatenation sum

Logic Level 3

The number 123456789 is concatenated 1729 times to form a certain number:

\[A = \underbrace{\overline{123456789123456789\dots 123456789}}_{\text{1729 } (123456789)\text{'s}} \]

Similarly, the number 987654321 is concatenated 1729 times to form another certain number:

\[B=\underbrace{\overline{987654321987654321\dots 987654321}}_{\text{1729 } (987654321)\text{'s}}\]

If \(A+B = C\), find the sum of digits of \(C\).

Bonus: Generalize this.

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