Question

The sum of first 'n' natural numbers is

• A. \(Σn=\frac {n(n-1)}{2}\)
• B. \(Σn=\frac {n(n+1)}{2}\)
• C. \(Σn=\frac {n(1-n)}{2}\)
• D. \(Σn=\frac {n^2(n+1)^2}{2}\)

Answer 1

The Correct Option is B

1. Understanding the Sum of First n Natural Numbers:
The sum of the first n natural numbers is a well-known mathematical formula:

$ \sum_{k=1}^{n} k = \frac{n(n + 1)}{2} $

2. Evaluating the Given Options:
Let’s quickly go over the choices:

• Option (1): $ \frac{n(n - 1)}{2} $ — This gives the sum of first (n − 1) natural numbers.
• Option (2): $ \frac{n(n + 1)}{2} $ — This is the correct formula.
• Option (3): $ \frac{n(1 - n)}{2} $ — This is a rearranged negative version, not correct.
• Option (4): $ \frac{n^2(n+1)^2}{4} $ — This is incorrect and overcomplicates the expression.

 

3. Example Check (Optional for Validation):
If n = 5, then the sum should be:
$ 1 + 2 + 3 + 4 + 5 = 15 $
Using Option (2):
$ \frac{5(5+1)}{2} = \frac{30}{2} = 15 $ ✔️

Final Answer:
The correct formula is $ \frac{n(n + 1)}{2} $