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A-LevelFurther MathematicsSummation of series9231/12 · May/June 2011 · Q15 Marks

Express 1/((2r + 1)(2r + 3)) in partial fractions and hence use the method of differences to find Σᵣ₌₁ⁿ 1/((2r + 1)(2r + 3)) .

  1. Express 1/((2r + 1)(2r + 3)) in partial fractions and hence use the method of differences to find Σᵣ₌₁ⁿ 1/((2r + 1)(2r + 3)) .[4]
  2. Deduce the value of Σᵣ₌₁^(∞) 1/((2r + 1)(2r + 3)) .[1]

Mark scheme

Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.

  1. [B1] Any method including cover-up rule.
  2. [M1A1] Expresses all terms as differences.
  3. [A1] Finds sum. (acf)
  4. [A1] S_inf = 1/6 (B0M1A1√ A0A1√ if signs reversed.)

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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 2011 Paper 1 Variant 2, question 1.

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