# The root of all digits

Number Theory Level 3

The digital root (also repeated digital sum) of a non-negative integer is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.

For example, the digital root of $$487$$ is $$1$$:

$$4+8+7=19$$

$$1+9=10$$

$$1+0=1$$

What is the digital root of $$123,456,\ldots,497,498,499,500$$?

Note: The number above is a base 10 number in which the digits are formed from consecutive integers from 1 to 500.

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