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A-LevelFurther MathematicsSummation of series9231/12 · May/June 2024 · Q38 Marks

Use standard results from the list of formulae (MF19) to show that Σ (from r=1 to N) r(r+1)(3r+4) = (1/4)N(N+1)(N+2)(9N+19).

  1. (a)Use standard results from the list of formulae (MF19) to show that Σ (from r=1 to N) r(r+1)(3r+4) = (1/4)N(N+1)(N+2)(9N+19).[3]
  2. (b)Express (3r+4)/(r(r+1)) in partial fractions and hence use the method of differences to find Σ (from r=1 to N) (3r+4)/(r(r+1)) * (1/4)ʳ⁺¹ in terms of N.[4]
  3. (c)Deduce the value of Σ (from r=1 to infinity) (3r+4)/(r(r+1)) * (1/4)ʳ⁺¹.[1]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [B1] Expands.
  2. [M1] Substitutes formulae from MF19.
  3. [A1] AG
  4. [M1 A1] Finds partial fractions.
  5. [M1] Writes at least three terms, including last.
  6. [A1] (1/4) - (1/(4ⁿ⁺¹(N+1)))
  7. [B1] 1/4 CAO

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About this question

Topic
Summation of series, A-Level Further Mathematics (syllabus 9231). Structured question, 8 marks.
Source
A-Level Further Mathematics, May/June 2024 Paper 1 Variant 2, question 3.

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