Sorry Iposted that previous question wrong.
Here is the right question.
What is the remainder when the sum of the first 102 counting numbers is divided by 5250.
the sum of the first 102 counting numbers is 102*103/2=10506/2=5253.
So the remainder divided by 5250 is 3.
No problem! To find the remainder when the sum of the first 102 counting numbers is divided by 5250, we can use the formula for the sum of an arithmetic series. The formula is given by:
Sn = (n/2) * (a + l),
where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
In this case, we want to find the sum of the first 102 counting numbers. The first term, a, is 1, and the last term, l, is 102. Let's substitute these values into the formula and calculate the sum:
Sn = (102/2) * (1 + 102)
= 51 * 103
= 5253
So, the sum of the first 102 counting numbers is 5253.
Now, we need to find the remainder when this sum is divided by 5250. We can do this by performing the division and finding the remainder:
Remainder = 5253 % 5250
= 3
Therefore, the remainder when the sum of the first 102 counting numbers is divided by 5250 is 3.