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A-LevelFurther MathematicsSummation of series9231/12 · Oct/Nov 2019 · Q59 Marks

Let SN = sum from r=1 to N of (5r + 1)(5r + 6) and TN = sum from r=1 to N of 1/((5r + 1)(5r + 6))

  1. (i)Use standard results from the List of Formulae (MF10) to show that SN = N(25N² + 90N + 83).[3]
  2. (ii)Use the method of differences to express TN in terms of N.[4]
  3. (iii)Find lim (N-3SNTN) as N->∞.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [M1] Expands.
  2. [M1] Substitutes formulae for Σr and Σr².
  3. [A1] Simplifies to the given answer (AG).
  4. [M1 A1] Finds partial fractions.
  5. [M1] Expresses terms as differences.
  6. [A1] At least 3 terms including last.
  7. [M1 A1] Divides S_N by N^3 and takes limits as N→∞

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About this question

Topic
Summation of series, A-Level Further Mathematics (syllabus 9231). Structured question, 9 marks.
Source
A-Level Further Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 5.

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