Natural Numbers Sum Formula Explained
The question asks for the formula representing the sum of the first '$n$' natural numbers.
Natural numbers are the positive integers starting from 1: {$1, 2, 3, 4, \dots$}.
We need to find the sum of the series:
- $S_n = 1 + 2 + 3 + \dots + n$
This is a standard arithmetic progression. The formula for the sum of the first '$n$' natural numbers is a well-known result in mathematics.
The formula is given by:
Comparing this standard formula with the given options:
- Option 1: $\frac{n(n + 1)}{2}$ - Matches the standard formula.
- Option 2: $\frac{n(n - 1)}{2}$ - Incorrect.
- Option 3: $\frac{n}{2}$ - Incorrect.
- Option 4: $\frac{n}{2} + 1$ - Incorrect.
Therefore, the correct formula for the sum of the first '$n$' natural numbers is $\frac{n(n + 1)}{2}$.
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Which of the above statements is/are correct ?
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