What will be the value of (1+2+3+\cdots+100)?
Answer and explanation
Correct answer: 5050
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Here, \(n=100\), so \(\frac{100\times101}{2}=50\times101=5050\). Therefore, 5050 is correct. The value 5000 results from using \(100\times50\) without the required adjustment for the \(101\) factor. Exam tip: For sums from \(1\) to \(n\), first write \(\frac{n(n+1)}{2}\), then substitute \(n\).
Frequently asked questions
What is the correct answer to this question?
5050
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Here, \(n=100\), so \(\frac{100\times101}{2}=50\times101=5050\). Therefore, 5050 is correct. The value 5000 results from using \(100\times50\) without the required adjustment for the \(101\) factor. Exam tip: For sums from \(1\) to \(n\), first write \(\frac{n(n+1)}{2}\), then substitute \(n\).
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.
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