What is the formula for the sum of the first n natural numbers?

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The formula for the sum of the first n natural numbers is derived from the pattern observed in the sequence of these numbers. When you add the numbers from 1 to n, you can pair them strategically to simplify the calculation.

For example, if n is 5, the sum would be 1 + 2 + 3 + 4 + 5. Pairing the first and the last number (1 + 5), the second and the second last (2 + 4), and leaving the middle number (3) gives you the same total as multiplying the number of pairs by their sum.

The formula is expressed as (n * (n + 1)) / 2. This works because you have n terms, and when you sum them effectively, you end up counting each pair from both ends of the sequence, leading to the average of (n + 1). Since pairs yield the same result through this strategy, dividing by 2 gives you the total sum.

Thus, the correct option accurately encapsulates this reasoning, making it the right choice.