1. The problem is to find the sum of all natural numbers from 1 to a given number $n$. 2. The formula to find the sum of the first $n$ natural numbers is: $$ S = \frac{n(n+1)}{2} $$ This formula works because the sum of pairs from the start and end of the sequence always equals $n+1$. 3. For example, if $n=10$, then: $$ S = \frac{10(10+1)}{2} = \frac{10 \times 11}{2} = 55 $$ 4. This means the sum of numbers from 1 to 10 is 55. 5. This formula is very useful because it allows you to quickly calculate the sum without adding each number individually. 6. Always remember that $n$ must be a natural number (positive integer) for this formula to apply. Final answer: The sum of the first $n$ natural numbers is $$\frac{n(n+1)}{2}$$.