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A-LevelFurther MathematicsSummation of series9231/12 · May/June 2019 · Q25 Marks

Let un = 4 sin(n-½) sin ½ / (cos(2n-1) + cos 1)

  1. (i)Using the formulae for cos P ± cos Q given in the List of Formulae MF10, show that un = 1/cos n - 1/cos(n-1)[2]
  2. (ii)Use the method of differences to find ΣN n=1 un.[2]
  3. (iii)Explain why the infinite series u₁ + u₂ + u3 + ... does not converge.[1]

Mark scheme

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

  1. [1] Uses formulae for cos P±cos Q.
  2. [1] AG
  3. [1] Applies (i), shows enough terms and cancellation.
  4. [1]
  5. [1] States "oscillates” or refers to diverging values of cos N.

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About this question

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

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