MCQ practice · SSC General Mathematics Board questions · Chapter 13: Finite Series
Which of the following is correct?
Think it through first, then pick an option.
- a (1 + 2 + 3 + ... + n)² = 441
- b (1 + 2 + 3 + ... + n²) = 441
- c 1² + 2² + 3² + ... + n² = 441
- d 1 + 2 + 3 + ... + n = 441
Answer and explanation
Correct answer: a (1 + 2 + 3 + ... + n)² = 441
1³ + 2³ + ... + n³ = (1 + 2 + ... + n)², so the equation is (1 + 2 + ... + n)² = 441.
Why the other options are wrong
- b (1 + 2 + 3 + ... + n²) = 441: This adds natural numbers up to n², which is not the sum of cubes.
- c 1² + 2² + 3² + ... + n² = 441: This is the sum of squares; the question gives the sum of cubes.
- d 1 + 2 + 3 + ... + n = 441: This is the sum of the numbers, not of their cubes.
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