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Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The sum of the first n natural numbers is given by n(n+1)/2.
(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.
(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².
(i) (ii) (iii)
(i) The sum of the first n natural numbers is given by n(n+1)/2.
(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.
(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².
(i) (ii) (iii)
- a)(i)-T, (ii)-T, (iii)-T
- b)(i)-T, (ii)-F, (iii)-T
- c)(i)-F, (ii)-T, (iii)-F
- d)(i)-T, (ii)-T, (iii)-F
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Read the given statements carefully and state T for true and F for fal...
(i) The sum of the first n natural numbers is indeed given by n(n+1)/2, which is correct.
(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6, which is also correct.
(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)², which is correct.
(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6, which is also correct.
(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)², which is correct.
Most Upvoted Answer
Read the given statements carefully and state T for true and F for fal...
Explanation of the Statements
Let's analyze each statement one by one:
Statement (i): The sum of the first n natural numbers is given by n(n+1)/2.
- This statement is True.
- The formula n(n+1)/2 accurately calculates the sum of the first n natural numbers.
- For example, for n=3, the sum is 1 + 2 + 3 = 6, and using the formula: 3(3+1)/2 = 6.
Statement (ii): The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.
- This statement is also True.
- The formula n(n+1)(2n+1)/6 correctly gives the sum of the squares of the first n natural numbers.
- For n=3, the squares are 1^2 + 2^2 + 3^2 = 14, and using the formula: 3(3+1)(2*3+1)/6 = 14.
Statement (iii): The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².
- This statement is True.
- The sum of the cubes of the first n natural numbers can be expressed as the square of the sum of the first n natural numbers.
- For n=3, the cubes are 1^3 + 2^3 + 3^3 = 36, and using the formula: (3(3+1)/2)² = 36.
Conclusion
- Since all three statements are true, the correct answer is option a: (i)-T, (ii)-T, (iii)-T.
Let's analyze each statement one by one:
Statement (i): The sum of the first n natural numbers is given by n(n+1)/2.
- This statement is True.
- The formula n(n+1)/2 accurately calculates the sum of the first n natural numbers.
- For example, for n=3, the sum is 1 + 2 + 3 = 6, and using the formula: 3(3+1)/2 = 6.
Statement (ii): The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.
- This statement is also True.
- The formula n(n+1)(2n+1)/6 correctly gives the sum of the squares of the first n natural numbers.
- For n=3, the squares are 1^2 + 2^2 + 3^2 = 14, and using the formula: 3(3+1)(2*3+1)/6 = 14.
Statement (iii): The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².
- This statement is True.
- The sum of the cubes of the first n natural numbers can be expressed as the square of the sum of the first n natural numbers.
- For n=3, the cubes are 1^3 + 2^3 + 3^3 = 36, and using the formula: (3(3+1)/2)² = 36.
Conclusion
- Since all three statements are true, the correct answer is option a: (i)-T, (ii)-T, (iii)-T.
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Question Description
Read the given statements carefully and state T for true and F for false.(i) The sum of the first n natural numbers is given by n(n+1)/2.(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².(i) (ii) (iii)a)(i)-T, (ii)-T, (iii)-Tb)(i)-T, (ii)-F, (iii)-Tc)(i)-F, (ii)-T, (iii)-Fd)(i)-T, (ii)-T, (iii)-FCorrect answer is option 'A'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Read the given statements carefully and state T for true and F for false.(i) The sum of the first n natural numbers is given by n(n+1)/2.(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².(i) (ii) (iii)a)(i)-T, (ii)-T, (iii)-Tb)(i)-T, (ii)-F, (iii)-Tc)(i)-F, (ii)-T, (iii)-Fd)(i)-T, (ii)-T, (iii)-FCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the given statements carefully and state T for true and F for false.(i) The sum of the first n natural numbers is given by n(n+1)/2.(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².(i) (ii) (iii)a)(i)-T, (ii)-T, (iii)-Tb)(i)-T, (ii)-F, (iii)-Tc)(i)-F, (ii)-T, (iii)-Fd)(i)-T, (ii)-T, (iii)-FCorrect answer is option 'A'. Can you explain this answer?.
Read the given statements carefully and state T for true and F for false.(i) The sum of the first n natural numbers is given by n(n+1)/2.(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².(i) (ii) (iii)a)(i)-T, (ii)-T, (iii)-Tb)(i)-T, (ii)-F, (iii)-Tc)(i)-F, (ii)-T, (iii)-Fd)(i)-T, (ii)-T, (iii)-FCorrect answer is option 'A'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Read the given statements carefully and state T for true and F for false.(i) The sum of the first n natural numbers is given by n(n+1)/2.(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².(i) (ii) (iii)a)(i)-T, (ii)-T, (iii)-Tb)(i)-T, (ii)-F, (iii)-Tc)(i)-F, (ii)-T, (iii)-Fd)(i)-T, (ii)-T, (iii)-FCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the given statements carefully and state T for true and F for false.(i) The sum of the first n natural numbers is given by n(n+1)/2.(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².(i) (ii) (iii)a)(i)-T, (ii)-T, (iii)-Tb)(i)-T, (ii)-F, (iii)-Tc)(i)-F, (ii)-T, (iii)-Fd)(i)-T, (ii)-T, (iii)-FCorrect answer is option 'A'. Can you explain this answer?.
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