What is the remainder when the sum of the first 102 counting numbers is divided by 5250?
To find the remainder when the sum of the first 102 counting numbers is divided by 5250, we need to calculate the sum.
The sum of the first n counting numbers can be found using the formula:
sum = (n/2) * (first number + last number)
In this case, n = 102, the first number is 1, and the last number is 102. Plugging these values into the formula:
sum = (102/2) * (1 + 102)
= 51 * 103
= 5253
Now, to find the remainder when the sum is divided by 5250, we perform the division and consider the remainder:
remainder = 5253 % 5250
= 3
Therefore, the remainder when the sum of the first 102 counting numbers is divided by 5250 is 3.