For each positive integer n, let `S_n`=sum of all positive integers less than or equal on n. Then `S_(51)` equals

Options

A. 50
B. 51
C. 1250
D. 1326

Explanation

To find \( S_{51} \), which is the sum of all positive integers less than or equal to 51, we can use the formula for the sum of the first \( n \) natural numbers:

\[ S_n = \frac{n(n + 1)}{2} \]

### Step-by-Step Solution:

1. **Identify \( n \)**: In this case, \( n = 51 \).

2. **Substitute \( n \) into the formula**:
\[ S_{51} = \frac{51(51 + 1)}{2} \]

3. **Calculate \( 51 + 1 \)**:
\[ 51 + 1 = 52 \]

4. **Multiply \( 51 \) by \( 52 \)**:
\[ 51 \times 52 = 2652 \]

5. **Divide the result by 2**:
\[ S_{51} = \frac{2652}{2} = 1326 \]

Thus, the value of \( S_{51} \) is \( 1326 \).

### Final Answer:
\[ S_{51} = 1326 \]