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Find the sum of the first n natural numbers: 1 + 2 + 3 + 4 + 5 + ... +n is given by (n/2)(n + 1).​

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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).

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