If n =100 then 899-100=799
therefore 799 numbers are there which are not divisible by 9 and
S=n(a + l) /2
S=799(108+999) /2
S=799×1107/2
S=884493/2
S=442246.5
is the sum

Introduction:
To find the sum of all three-digit numbers that are not divisible by 9, we need to first identify the range of numbers within this criteria. Then, we can calculate the sum of these numbers using a mathematical formula.

Identifying the Range:
The three-digit numbers range from 100 to 999. To determine which numbers are not divisible by 9, we can check if their sum of digits is divisible by 9. If the sum of digits is divisible by 9, then the number itself is divisible by 9.

Calculating the Sum:
To calculate the sum of all three-digit numbers that are not divisible by 9, we can use the arithmetic series formula. The formula for the sum of an arithmetic series is:
Sum = (n/2)(first term + last term)

Breaking Down the Calculation:
1. First, let's find the number of terms within our range that are not divisible by 9.
- From 100 to 999, there are 900 three-digit numbers in total.
- Out of these, the numbers divisible by 9 are:
- 108, 117, 126, ..., 990, 999
- To find the number of terms not divisible by 9, we subtract the divisible numbers from the total:
- Number of terms not divisible by 9 = 900 - 100 = 800

2. Next, we need to find the first and last terms of the series, which are the smallest and largest three-digit numbers not divisible by 9.
- The smallest three-digit number not divisible by 9 is 100.
- The largest three-digit number not divisible by 9 is 999.

3. Now, we can substitute the values into the formula and calculate the sum.
- n = 800 (number of terms not divisible by 9)
- first term = 100
- last term = 999

Sum = (800/2)(100 + 999) = 400(1099) = 439,600

Conclusion:
The sum of all three-digit numbers that are not divisible by 9 is 439,600.