1. The problem is to find the sum of integers from 1 to $n$. 2. The formula to find the sum of the first $n$ integers is given by the arithmetic series sum formula: $$ S = \frac{n(n+1)}{2} $$ 3. This formula works because the sum of the first and last number is $1 + n$, the second and second last is $2 + (n-1)$, and so on, pairing up to $n/2$ pairs each summing to $n+1$. 4. For example, if $n=5$, the sum is: $$ S = \frac{5(5+1)}{2} = \frac{5 \times 6}{2} = 15 $$ 5. So, the sum of integers from 1 to $n$ is always $\frac{n(n+1)}{2}$, which is a quick and efficient way to calculate it without adding each number individually.