Question

The sum of the first \(n\) natural numbers is:

• A. \( \frac{n(n+1)}{2} \)
• B. \( \frac{n(n-1)}{2} \)
• C. \( n^2 \)
• D. \( n(n+1) \)

Hint:

To find the sum of the first \(n\) natural numbers, use the formula \( \frac{n(n+1)}{2} \).

Answer 1

The Correct Option is A

The sum of the first \(n\) natural numbers is given by the formula: \[ S_n = 1 + 2 + 3 + \dots + n = \frac{n(n+1)}{2} \] This is a well-known formula that can be derived by pairing the terms from the first and last elements in the sum. For example: \[ (1 + n), (2 + n-1), (3 + n-2), \dots \] Each pair adds up to \(n+1\), and there are \(n/2\) such pairs, so the total sum is: \[ S_n = \frac{n(n+1)}{2} \] Thus, the sum of the first \(n\) natural numbers is \( \frac{n(n+1)}{2} \).