The sum of the first 20 positive integers can be calculated using the formula for the sum of an arithmetic series:

$S_n = \frac{n}{2} \times (a + l)$

where:

• $n$ is the number of terms,
• $a$ is the first term,
• $l$ is the last term.

For the first 20 integers:

• $n = 20$,
• $a = 1$ (the first term),
• $l = 20$ (the last term).

Substituting these values into the formula:

$S_{20} = \frac{20}{2} \times (1 + 20) = 10 \times 21 = 210$

Thus, the sum of the first 20 positive integers is 210.

Would you like a more detailed explanation or have any other questions? Here are a few related questions you can explore:

1. How can the formula for the sum of an arithmetic series be derived?
2. What is the sum of the first 100 positive integers?
3. How would you calculate the sum of integers from 50 to 150?
4. What happens if we change the first term in the series to a different value?
5. How do you find the sum of an arithmetic series with a common difference of 3?

Tip: The sum of integers from 1 to $n$ is always given by the formula $S_n = \frac{n(n+1)}{2}$, which is quicker than using the general formula for some simple cases.