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A-LevelFurther MathematicsSummation of series9231/12 · Oct/Nov 2014 · Q15 Marks

Given that Uk = 1/√(2k-1) - 1/√(2k+1), express ∑(from k=1 to n) Uk in terms of n. Deduce the value of ∑(from k=1 to ∞) Uk

  1. mainGiven that Uk = 1/√(2k-1) - 1/√(2k+1), express ∑(from k=1 to n) Uk in terms of n. Deduce the value of ∑(from k=1 to ∞) Uk[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

  1. [M1A1] (1/√1 - 1/√3) + (1/√3 - 1/√5) + ... + (1/√(2n-1) - 1/√(2n+1))
  2. [M1A1] = 1 - 1/√(2n+1)
  3. [B1] 1

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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, Oct/Nov 2014 Paper 1 Variant 2, question 1.

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