2001 APMO Problems/Problem 1
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For any positive integer , let
be the sum of digits in the decimal representation of
. Any positive integer obtained by removing one or more digits from the right end of the decimal representation of
is called a stump of
. Let
be the sum of all stumps of
. Prove that
. (For example, if
, we have
, and stumps
and
, so
. We verify that
.)