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Sum of First n Natural Numbers
publish date: 2026/05/23 05:43:43.368245 UTC
Gauss showed that the sum \(S = 1 + 2 + 3 + \cdots + n\) can be expressed as a closed formula. Enter this formula below.
Correct Answer
$\frac{n(n+1)}{2}$
Explanation
By writing \(S\) in both ascending and descending order and adding term by term, we get \(2S = n(n+1)\), so \(S = \frac{n(n+1)}{2}\). This elegant proof shows how algebra simplifies what would otherwise be a cumbersome arithmetic calculation.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012