Which is correctly written for the sum (1+2+3+\cdots+n)?
Answer and explanation
Correct answer: \(\frac{n(n+1)}{2}\)
The sum of the first \(n\) natural numbers is \(1+2+3+\cdots+n=\frac{n(n+1)}{2}\), so option A is correct. \(\frac{n(n-1)}{2}\) equals the sum of the first \(n-1\) natural numbers, making it a close but incorrect distractor. Exam tip: verify the formula with a small value such as \(n=3\); both the sum and \(\frac{3\times4}{2}\) give \(6\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{n(n+1)}{2}\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(1+2+3+\cdots+n=\frac{n(n+1)}{2}\), so option A is correct. \(\frac{n(n-1)}{2}\) equals the sum of the first \(n-1\) natural numbers, making it a close but incorrect distractor. Exam tip: verify the formula with a small value such as \(n=3\); both the sum and \(\frac{3\times4}{2}\) give \(6\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
