Choose a digit from 1-9 Make numbers that add to 1000 using only the digit you chose You can only use your digit eight times?

The sum 9 + 99 + 999 + 9999 + 99 999 + ....

where the last number to be added consists of nine digits of 9 becomes:

(10 – 1) + (100 – 1) + (1000 – 1) + (10 000 – 1) + ...

where the last multiple of 10 has nine zeros.

There are nine pairs of brackets altogether.

Add the multiples of 10 first and then subtract 9:

The digit 1 appears 9 times in the final answer.