plumiSeries: standard sums: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 4.2 Series: standard sums, 2018–2025, 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 2025, AS Core Pure, Q8 (7 marks): The first n triangular numbers are 1, 3, 6, 10, ... , 1 2 n(n + 1) where n is a positive integer. (a) Use the standard results for 2 1 n r r and 1 n r r to show
- June 2024, AS Core Pure, Q3 (10 marks): (a) Use the standard results for summations to show that, for all positive integers n, r r n n n an b r n 2 1 1 1 12 1 2 where a and b are integers to be dete
- June 2023, Core Pure 1, Q7 (12 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (a) Explain why, for n ∈ 1 2 2 1
- June 2023, AS Core Pure, Q8 (8 marks): (a) Use the standard results for r n 1 r 2 and r n 1 r to show that, for all positive integers n, ( ) ( ) 2 1 3 1 2 2 1 r n an r n where a is a constant to be d
- June 2022, AS Core Pure, Q5 (12 marks): (a) Use the standard summation formulae to show that, for n ∈ , 3 17 25 2 2 1 r r n n An B r n − − ( ) = − − ( ) =∑ where A and B are integers to be determine
- November 2021, Core Pure 2, Q4 (9 marks): In this question you may assume the results for r r n 3 1 =∑ , r r n 2 1 =∑ and r r n =∑ 1 (a) Show that the sum of the cubes of the first n positive odd number
- November 2020, AS Core Pure, Q5 (7 marks): r (r + 2) (r + 1) Figure 2 A block has length (r + 2) cm, width (r + 1) cm and height r cm, as shown in Figure 2. In a set of n such blocks, the first block has
- June 2018, AS Core Pure, Q6 (10 marks): (a) Use the standard results for r r r n r n 2 1 1 = = ∑ ∑ and to show that ( ) 3 2 1 2 6 3 1 2 1 2 r n n n r n − = − − =∑ for all positive integers n. (5
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