plumiSeries: standard sums: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on D.2 Series: standard sums, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 8 questions on Series: standard sums, as a list
- June 2024, Paper 2, Q5 (3 marks): The first four terms of the series S can be written as S = (1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + ... 5 (a) Write an expression, using ∑ notation, for the sum
- June 2023, Paper 2, Q7 (3 marks): Show that X n+1 r=11 r3 = 1 4 (n2 + an + b)(n2 + an + c) where a, b and c are integers to be found. [3 marks]
- June 2023, AS Paper 1, Q13 (10 marks): (a) Prove by induction that, for all integers n ≥ 1, n r =1 r2 = 1 6 n(n + 1)(2n + 1) [4 marks] 13 (c) Use the formula in part (a) to write down a factorised
- November 2021, Paper 1, Q1 (1 mark): Find X 20 r=1 (r2 − 2r) Circle your answer. [1 mark] 2450 2660 5320 43680
- November 2021, Paper 2, Q4 (7 marks): (a) Show that (r + 1)2 − r2 = 2r + 1 [1 mark] 4 (b) Use the method of differences to show that X n r=1 (2r + 1) = n2 + 2n [3 marks] 4 (c) Verify that using the
- November 2021, AS Paper 1, Q9 (7 marks): (a) Use the standard formulae for X n r=1 r and X n r=1 r2 to show that X n r=1 r(r + 3) = an(n + 1)(n + b) where a and b are constants to be determined. [4 mar
- November 2020, Paper 2, Q6 (5 marks): Find the sum of all the integers from 1 to 999 inclusive that are not square or cube numbers. [5 marks]
- June 2019, Paper 2, Q4 (3 marks): The positive integer k is such that X k r=1 (3r − k) = 90 Find the value of k. [3 marks]
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