Question:
The sum of the first \(n\) natural numbers is:
The sum of the first \(n\) natural numbers is:
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To find the sum of the first \(n\) natural numbers, use the formula \( \frac{n(n+1)}{2} \).
Updated On: May 13, 2025
- \( \frac{n(n+1)}{2} \)
- \( \frac{n(n-1)}{2} \)
- \( n^2 \)
- \( n(n+1) \)
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The Correct Option is A
Solution and Explanation
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 \( \frac{n(n+1)}{2} \).
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