1. The problem is to find the formula for the sum of the first $n$ natural numbers, i.e., $s = 1 + 2 + 3 + \cdots + n$. 2. We can use the formula for the sum of an arithmetic series. The first term $a_1 = 1$, the last term $a_n = n$, and the number of terms is $n$. 3. The sum of an arithmetic series is given by: $$ s = \frac{n}{2} (a_1 + a_n) $$ 4. Substitute $a_1 = 1$ and $a_n = n$: $$ s = \frac{n}{2} (1 + n) $$ 5. Simplify the expression: $$ s = \frac{n(n+1)}{2} $$ 6. Therefore, the sum of the first $n$ natural numbers is: $$ s = \frac{n(n+1)}{2} $$