Find the sum of first `n` natural numbers.

Answer

To find the sum of the first \( n \) natural numbers, we can follow these steps:

### Step 1: Identify the series
The first \( n \) natural numbers are:
\[ 1, 2, 3, \ldots, n \]

### Step 2: Recognize the series as an Arithmetic Progression (AP)
The series is an AP where:
- The first term \( a = 1 \)
- The common difference \( d = 1 \)

### Step 3: Use the formula for the sum of the first \( n \) terms of an AP
The formula for the sum \( S_n \) of the first \( n \) terms of an AP is given by:
\[ S_n = \frac{n}{2} \times (2a + (n - 1)d) \]

### Step 4: Substitute the values into the formula
Substituting \( a = 1 \) and \( d = 1 \) into the formula:
\[ S_n = \frac{n}{2} \times (2 \times 1 + (n - 1) \times 1) \]

### Step 5: Simplify the expression
Now simplify the expression:
\[ S_n = \frac{n}{2} \times (2 + n - 1) = \frac{n}{2} \times (n + 1) \]

### Step 6: Final result
Thus, the sum of the first \( n \) natural numbers is:
\[ S_n = \frac{n(n + 1)}{2} \]