Answer: Since there are n/2 pairs, the sum of these pairs is (n/2)(n + 1).
Step-by-step explanation: The formula (n/2)(n + 1) can be used to calculate the sum of the first n natural numbers, 1 + 2 + 3 + 4 + 5 +... + n. This equation was created using a pattern found in the sums of successive numbers.
Consider adding the first n natural numbers to gain an understanding of this formula. We can discern a pattern if we write the numbers backward:
n + (n-1) + (n-2) + ... + 2 + 1
We can see that each pair adds up to n+1 if we pair the first and last terms, the second and next-to-last terms, and so on:
(n + 1) + (n + 1) + ... + (n + 1)
Given that there are n/2 pairs, their sum equals (n/2)(n + 1).
Hence, the sum of the first n natural numbers can be calculated as (n/2)(n + 1).