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Question 210044
JEE Mathematics · Hard

Sequences and Series: Sum formula MCQ

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Sum formulaHardQuestion 210044

Question

The sum of n terms of the series whose nth term is n² + n + 1 is:
  1. A
    n(n+1)(n+2)/3 + n
  2. B
    n(n²+2n+3)/3
  3. C
    n(n+1)(2n+1)/6 + n(n+1)/2 + n
  4. D
    All of these are equivalent
    Correct

Correct answer

All of these are equivalent

Explanation

Sₙ = Σ(n²+n+1) = n(n+1)(2n+1)/6 + n(n+1)/2 + n = n[n(2n+1)/6 + (n+1)/2 + 1]. These simplify to the same expression.

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