The sum of series `1+2+3+4+…………+998+999+1000` is

Options

A. 5050
B. 500500
C. 550000
D. 55000

Answer

To find the sum of the series \(1 + 2 + 3 + 4 + \ldots + 998 + 999 + 1000\), we can use the formula for the sum of the first \(n\) natural numbers, which is given by:

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

### Step-by-Step Solution:

1. **Identify \(n\)**: In this case, we are summing the first 1000 natural numbers, so \(n = 1000\).

2. **Apply the formula**: Substitute \(n\) into the formula:
\[ S_{1000} = \frac{1000(1000 + 1)}{2} \]

3. **Calculate \(1000 + 1\)**:
\[ 1000 + 1 = 1001 \]

4. **Multiply \(1000\) and \(1001\)**:
\[ 1000 \times 1001 = 1001000 \]

5. **Divide by \(2\)**:
\[ S_{1000} = \frac{1001000}{2} = 500500 \]

Thus, the sum of the series \(1 + 2 + 3 + 4 + \ldots + 998 + 999 + 1000\) is \(500500\).

### Final Answer:
\[ \text{The sum of the series is } 500500. \]

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