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6 marksSeries

CAPE Pure Mathematics Unit 2 · May/June 2024 · Paper 2 · Question 4(d)

Use the sum of a series to calculate an equivalent fraction for the repeating decimal 0.2727272...

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Other parts of this question

  1. 4(a)(i)Use the intermediate value theorem to prove that f(x) = 2x³ + x² + 9x - 5 has at least one root in the interval [0.2, 1].[3 marks]
  2. 4(a)(ii)Hence, use three iterations of the interval bisection method to estimate the root of f in the interval [0.2, 1].[5 marks]
  3. 4(b)(i)Write down an expression for the nᵗʰ term of the sequence.[4 marks]
  4. 4(b)(ii)Determine whether the sequence converges or diverges.[3 marks]
  5. 4(c)Calculate ∑(from r=0 to 27) r.[4 marks]

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