
We can use the formula for the sum of an arithmetic series:
\[S = \frac{n}{2}(a + b),\]
where $S$ is the sum, $n$ is the number of terms, $a$ is the first term, and $b$ is the last term.

In this case, $n = 102$, $a = 1$, and $b = 102$, so the sum is:
\[S = \frac{102}{2}(1 + 102) = 51 \times 103 = 5253.\]

To find the remainder when $S$ is divided by 5250, we divide 5253 by 5250 and find that the remainder is $\boxed{3}$.

The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If the sum of the first 102 counting numbers is divided by 5250, what is the remainder?

### Answer:
