What is the sum of the first (64) natural numbers?
Answer and explanation
Correct answer: 2080
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Therefore, \(S_{64}=\frac{64\times65}{2}=32\times65=2080\). Hence, 2080 is correct. The value 2048 may result from using \(64\times32\), but that incorrectly omits the \((n+1)=65\) factor. Exam tip: Write \(n(n+1)/2\) and cancel the even factor with 2 first.
Frequently asked questions
What is the correct answer to this question?
2080
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Therefore, \(S_{64}=\frac{64\times65}{2}=32\times65=2080\). Hence, 2080 is correct. The value 2048 may result from using \(64\times32\), but that incorrectly omits the \((n+1)=65\) factor. Exam tip: Write \(n(n+1)/2\) and cancel the even factor with 2 first.
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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