Sums of elementary series — A/L Combined Mathematics

How do I practise Sums of elementary series?

1 question with a worked solution

Check before you answer: General Term Formulation: Finding the r-th term u_r from the given pattern of terms and expanding it as a polynomial in r.

1. What is the closed-form algebraic formula for the sum of the squares of the first n natural numbers, ∑_r=1ⁿ r²?
   1. A) [n(n + 1)] / 2
   2. B) [n(n + 1)(2n + 1)] / 6
   3. C) [n(n + 1) / 2]²
   4. D) [n(2n + 1)(2n - 1)] / 6
   Check my answer

   Correct answer: B) [n(n + 1)(2n + 1)] / 6

   The sum of the squares of the first n positive integers is given by the standard identity ∑_r=1ⁿ r² = [n(n + 1)(2n + 1)] / 6.

   Show worked solution

   Step 1: Standard mathematical series formula: ∑_r=1ⁿ r² = n(n + 1)(2n + 1) / 6. Answer: [n(n + 1)(2n + 1)] / 6.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Sums of elementary series fit in the syllabus?

Year 1 · Term 3