Find the sum of the series 1 + 4 + 9 +16 + 25 + 36 +......+ 121 ?
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Find the sum of the series 1 + 4 + 9 +16 + 25 + 36 +......+ 121 ?
- A.
506
- B.
523
- C.
525
- D.
None of these
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Concept: Sum of squares formula: n(n+1)(2n+1)/6
Recognize the series as squares: 1 + 4 + 9 + ... + 121 = 1^2 + 2^2 + ... + 11^2.
Apply the formula for the sum of squares: n(n+1)(2n+1)/6.
Substitute n = 11 into the formula: 11 × 12 × 23 / 6.
Calculate step by step: 11 × 12 = 132; 132 × 23 = 3036; 3036 ÷ 6 = 506.
Answer: 506