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1+2+3+4+…………+100=...

`1+2+3+4+…………+100=`

A

5000

B

5050

C

5500

D

5555

Text Solution

AI Generated Solution

The correct Answer is:
To find the sum of the first 100 natural numbers, we can use the formula for the sum of an arithmetic progression (AP). The sum \( S_n \) of the first \( n \) terms of an AP can be calculated using the formula: \[ S_n = \frac{n}{2} \times (a + l) \] where: - \( n \) is the number of terms, - \( a \) is the first term, - \( l \) is the last term. In this case: - The first term \( a = 1 \), - The last term \( l = 100 \), - The number of terms \( n = 100 \). Now, we can substitute these values into the formula: 1. **Calculate the sum**: \[ S_{100} = \frac{100}{2} \times (1 + 100) \] 2. **Simplify the expression**: \[ S_{100} = 50 \times 101 \] 3. **Perform the multiplication**: \[ S_{100} = 5050 \] Thus, the sum \( 1 + 2 + 3 + \ldots + 100 = 5050 \). ### Final Answer: The sum of the first 100 natural numbers is **5050**. ---
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