Find the sum of all integers between 1200 and 2900, inclusive, which are not divisible by 9.

9*134 = 1206

9*322 = 2898

So, subtract all the multiples of 9 from the total sum:

∑[k=1200,2900] k - ∑[k=134,322] 9k
= 3 487 050 - 387 828
= 3 099 222

To find the sum of all integers between 1200 and 2900, inclusive, which are not divisible by 9, you can follow these steps:

Step 1: Determine the range of integers between 1200 and 2900, inclusive.
- The range of integers is calculated by subtracting the smaller number from the larger number and adding 1.
- In this case, the range is 2900 - 1200 + 1 = 1701.

Step 2: Determine the number of integers within the range that are divisible by 9.
- To find the number of integers divisible by 9, we need to determine how many integer multiples of 9 fall within the range.
- The smallest multiple of 9 within the range is the first multiple greater than or equal to 1200, which is 1206.
- The largest multiple of 9 within the range is the last multiple less than or equal to 2900, which is 2907.
- To find the number of multiples of 9, we can calculate (2907 - 1206) / 9 + 1 = 171.
- Therefore, there are 171 integers within the range that are divisible by 9.

Step 3: Calculate the sum of integers divisible by 9.
- To find the sum of integers divisible by 9, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference.
- In this case, n = 171 (from previous step), a = 1206 (smallest multiple of 9), and d = 9 (common difference).
- Substituting these values into the formula, we get Sn = (171/2)(2(1206) + (171-1)9) = 87555.

Step 4: Calculate the sum of all integers in the given range.
- To find the sum of all integers in the range from 1200 to 2900, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference.
- In this case, n = 1701 (range of integers), a = 1200 (smallest integer in the range), and d = 1 (common difference).
- Substituting these values into the formula, we get Sn = (1701/2)(2(1200) + (1701-1)1) = 1978300.

Step 5: Calculate the sum of integers not divisible by 9.
- To find the sum of integers not divisible by 9, we subtract the sum of integers divisible by 9 from the sum of all integers in the range.
- Not divisible by 9 sum = Total sum - Divisible by 9 sum = 1978300 - 87555 = 1890745.

Therefore, the sum of all integers between 1200 and 2900, inclusive, which are not divisible by 9, is 1,890,745.