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If S(n) denotes the sum of digits of n, how can I prove that for any...

If S(n) denotes the sum of digits of n, how can I prove that for any n, the sequence n, S(n), S(S(n)),... eventually becomes constant? I understand that this is essentially just finding the digital sum of n, but I am having hard time figuring out how I would formally prove this. Any help is appreciated! Thanks!

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