Digit not contained by arithmetic mean of the nine distinct numbers in the given set {9,99,999,9999,99999,999999,9999999,99999999,999999999}

Explanation

writing the eqn `9 + 99 + 999 + ............ + 999999999`

`(10^1 -1) + (10^2-1) + (10^3-1) + .........+ (10^9-1)`

`= 10^1 + 10^2 + 10^3 + ........ + 10^9 - 9`

`= 10[(10^9-1)/(10-1)] - 9`

`= (10^10 - 10-81)/9 = (10^10-91)/9`

`= (10000000000 - 91)/9`

`= 9999999909/9 = 1111111101`

`AM = 1111111101/9 = 123456789`

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